Czichos H., Saito T., Smith L.E. (Eds.) Handbook of Metrology and Testing
Подождите немного. Документ загружается.
1148 Part E Modeling and Simulation Methods
2
1.8
1.6
1.4
1.2
1
0.8
0
52-site
50-site
40-site
34-site
26-site
0.02 0.04 0.06 0.08 0.1
δ
2
μ
Fig. 22.35 Scaling behavior of chemical potential μ as
a function of doping δ for the two-dimensional t-J model
(after [22.227])
experiments [22.224–226]. For the two-dimensional t-J
model, a similar analysis has been made based on the
numerical results obtained by a Monte Carlo power
method (Sect. 22.3.7) [22.227] as shown in Figs. 22.35
and 22.36. The results are qualitatively the same as
the Hubbard model. Here, compressibility κ behaves
as κ ∝∂δ/∂μ.
52-site
40-site
34-site
26-site
20-site
18-site
16-site
8
7
6
5
4
3
2
1
0
0 0.20.1 0.3 0.4 0.5 0.6 0.7
δ
2
S
max
(Q)
–1
Fig. 22.36 Scaling behavior of spin structure factor
S
max
(Q) as a function of doping δ for the two-dimensional
t-J model (after [22.227])
1
0.8
0.6
0.4
0.2
0
0 0.2 0.4 0.80.6 1
H/H
max
M/M
max
M
s
/M
max
H
c
/H
max
35-site
26-site
36-site
26-site
Fig. 22.37 Magnetization process of the S = 1/2 XXZ
model with Ising-like anisotropy on a square lattice
(after [22.228]). Solid and dotted lines denote the magneti-
zation jump determined by the Maxwell construction
These numerical simulations suggest that spin and
charge fluctuations diverge toward the Mott transition
point. There is a possibility that such large fluctuations
may lead to the high-T
c
superconductivity.
In this way, properties of strongly correlated elec-
tron systems can be investigated by quantum Monte
Carlo simulations.
22.7.3 Phase Separation
Quantum Monte Carlo simulations can also be applied
to investigate first-order phase transitions. For example,
in the two-dimensional t-J model, the phase-separation
boundary has been investigated by a Monte Carlo power
method [22.227] (Sect. 22.3.7). In finite systems, the
energy obtained in canonical ensembles as a function
of the electron density becomes concave downward in
the region of phase separation. In order to satisfy the
thermodynamic requirement, a tangent has to be drawn
based on the Maxwell construction. Thus, the phase-
separation boundary can be estimated using quantum
Monte Carlo data in finite clusters. Since very accu-
rate simulations are necessary in order to determine the
precise position of the phase-separation boundary in
the very small doping regime for the two-dimensional
t-J model, it is a subtle problem and still controver-
sial [22.227,229–239].
Part E 22.7
Monte Carlo Simulation References 1149
1
0.8
0.6
0.4
0.2
0
0 0.2 0.4 0.80.6 1
(λ–1)/(λ+1)
H
c
/H
max
2d
3d
1d
Classical
Fig. 22.38 Critical field H
c
for the S = 1/2 XXZ model
with Ising-like anisotropy (after [22.228]). Here, λ denotes
the anisotropy parameter. At the isotropic point, λ = 1
A similar analysis has been made for the mag-
netization process of the S = 1/2 XXZ models with
Ising-like anisotropy in two and three dimensions
by using the cluster algorithm [22.228] (Sect. 22.3.3).
Magnetization curves (M-H curves) are obtained by
the quantum Monte Carlo simulation in canonical en-
sembles in finite systems as shown in Fig. 22.37. This
figure shows the nonmonotonic behavior of magnetiza-
tion M as a function of magnetic field H, indicating
the phase separation (i. e., the magnetization jump).
The phase-separation boundary determined by the
Maxwell construction has little size effect as shown
in Fig. 22.37.
1
0.8
0.6
0.4
0.2
0
0 0.2 0.4 0.80.6 1
(λ–1)/(λ+1)
M
c
/M
max
2d
3d
Classical
Fig. 22.39 Magnetization jump M
s
for the S = 1/2 XXZ
model with Ising-like anisotropy (after [22.228])
The critical field H
c
and the magnetization jump
M
s
are shown in Figs. 22.38 and 22.39. The re-
sults in two and three dimensions are quite dif-
ferent from the one-dimensional result. In one di-
mension, there is no region of the phase separa-
tion, and the critical field near λ =1 behaves as
H
c
∝exp
−π
2
/2
√
2(λ −1)
[22.240], where λ denotes
the anisotropy parameter. (At the isotropic point, λ =1.)
It should be noted that the S = 1/2 XXZ model
can be mapped onto the Bose–Hubbard model with
nearest-neighbor repulsions in the hard-core limit.
Thus, numerical results for the S =1/2 XXZmodel im-
ply that the corresponding Bose–Hubbard model also
shows the first-order transition.
References
22.1 K. Binder, Q.W. Heermann: Monte Carlo Simulation
in Statistical Physics, Springer Series in Solid-State
Sciences (Springer, Berlin Heidelberg 1988) p. 80
22.2 N. Metropolis, A.W. Rosenbluth, M.N. Rosenbluth,
A.H. Teller, E. Teller: Equation of state calculations
by fast computing machines, J. Chem. Phys. 21,
1087–1092 (1953)
22.3 A.M. Ferrenberg, D.P. Landau, Y.J. Wong: Monte
Carlo simulations: Hidden errors from “good” ran-
dom number generators, Phys. Rev. Lett. 69,
3382–3384 (1992)
22.4 M. Matsumoto, Y. Kurita: Twisted GFSR generators,
ACMTrans.Model.Comput.Siml.2, 179–194 (1992)
22.5 M. Matsumoto, Y. Kurita: Twisted GFSR generators
II,ACMTrans.Model.Comput.Siml.4,254–266
(1994)
22.6 M. Matsumoto, T. Nishimura: Mersenne Twister:
A 623-dimensionally equidistributed uniform
pseudorandom number generator, ACM Trans.
Model. Comput. Siml. 8, 3–30 (1998)
22.7 The source codes in various languages and original
articles can be downloaded from the web-
Part E 22
1150 Part E Modeling and Simulation Methods
site http://www.math.sci.hiroshima-u.ac.jp/∼m-
mat/MT/emt.html
22.8 M. Suzuki: Linear and nonlinear dynamic scal-
ing relations in the renormalization group theory,
Phys. Lett. A 58, 435–436 (1976)
22.9 M. Suzuki: Static and dynamic finite-size scaling
theory based on the renormalization group ap-
proach, Prog. Theor. Phys. 83, 1142–1150 (1977)
22.10 N. Ito: Non-equilibrium critical relaxation of the
three-dimensional Ising model, Physica A 192,
604–616 (1993)
22.11 N. Ito, T. Matsuhisa, H. Kitatani: Ferromagnetic
transition of ±J Isingspinglassmodelonsquare
lattice, J. Phys. Soc. Jpn. 67, 1188–1196 (1998)
22.12 N. Ito, K. Hukushima, K. Ogawa, Y. Ozeki: Nonequi-
librium relaxation of fluctuations of physical
quantities, J. Phys. Soc. Jpn. 69, 1931–1934 (2000)
22.13 Z.B.Li,L.Schülke,B.Zheng:DynamicMonteCarlo
measurement of critical exponents, Phys. Rev. Lett.
74, 3396–3398 (1995)
22.14 Y. Nonomura: New quantum Monte Carlo approach
to ground-state phase transitions in quantum spin
systems, J. Phys. Soc. Jpn. 67, 5–7 (1998)
22.15 Y. Nonomura: New quantum Monte Carlo study
of quantum critical phenomena with Trotter-
number-dependent finite-size scaling and non-
equilibrium relaxation, J. Phys. A 31, 7939–7954
(1998)
22.16 T. Nakamura, Y. Ito: A quantum Monte Carlo algo-
rithm realizing an intrinsic relaxation, J. Phys. Soc.
Jpn. 72, 2405–2408 (2003)
22.17 Y. Ozeki, K. Ogawa, N. Ito: Nonequilibrium re-
laxation analysis of Kosterlitz–Thouless phase
transition, Phys. Rev. E 67, 026007(1–5) (2003)
22.18 Y. Ozeki, K. Kasono, N. Ito, S. Miyashita: Nonequi-
librium relaxation analysis for first-order phase
transitions, Physica A 321, 271–279 (2003)
22.19 Y. Iba: Extended ensemble Monte Carlo, Int. J. Mod.
Phys. C 12, 623–656 (2001)
22.20 A.M. Ferrenberg, R.H. Swendsen: New Monte Carlo
technique for studying phase transitions, Phys.
Rev. Lett. 61, 2635–2638 (1988)
22.21 A.M. Ferrenberg, R.H. Swendsen: Optimized Monte
Carlo data analysis, Phys. Rev. Lett. 63, 1195–1198
(1989)
22.22 A.M. Ferrenberg, D.P. Landau: Critical behavior
of the three-dimensional Ising model: A high-
resolution Monte Carlo study, Phys. Rev. B 44,
5081–5091 (1991)
22.23 B.A. Berg, T. Neuhaus: Multicanonical algorithms
for first order phase transitions, Phys. Lett. B 267,
249–253 (1991)
22.24 B.A. Berg, T. Neuhaus: Multicanonical ensemble:
A new approach to simulate first-order phase tran-
sitions, Phys. Rev. Lett. 68, 9–12 (1992)
22.25 J. Lee: New Monte Carlo algorithm: Entropic sam-
pling, Phys. Rev. Lett. 71, 211–214 (1993)
22.26 P.M.C. de Oliveira, T.J.P. Penna, H.J. Herrmann:
Broad histogram method, Braz. J. Phys. 26, 677–
683 (1996)
22.27 P.M.C. de Oliveira, T.J.P. Penna, H.J. Herrmann:
Broad histogram Monte Carlo, Eur. Phys. J. B 1,
205–208 (1998)
22.28 R.H.Swendsen,B.Diggs,J.-S.Wang,S.-T.Li,
C. Genovese, J.B. Kadane: Transition matrix
Monte Carlo, Int. J. Mod. Phys. C 10,1563–1569
(1999)
22.29 J.-S. Wang, T.K. Tay, R.H. Swendsen: Transition
matrix Monte Carlo reweighting and dynamics,
Phys. Rev. Lett. 82, 476–479 (1999)
22.30 J.-S. Wang: Flat histogram Monte Carlo method,
Physica A 281, 147–150 (2000)
22.31 F. Wang, D.P. Landau: Efficient, multiple-range
random walk algorithm to calculate the density of
states, Phys. Rev. Lett. 86, 2050–2053 (2001)
22.32 F. Wang, D.P. Landau: Determining the density of
states for classical statistical models: A random
walk algorithm to produce a flat histogram, Phys.
Rev. E 64,1–16(2001)
22.33 J. Lee, J.M. Kosterlitz: New numerical method to
study phase transitions, Phys. Rev. Lett. 65,137–140
(1990)
22.34 J. Lee, J.M. Kosterlitz: Finite-size scaling and Monte
Carlo simulations of first-order phase transitions,
Phys. Rev. B 43, 3265–3277 (1991)
22.35 R.H. Swendsen, J.-S. Wang: Nonuniversal critical
dynamics in Monte Carlo simulations, Phys. Rev.
Lett. 58,86–88(1987)
22.36 P.W. Kasteleyn, C.M. Fortuin: Phase transitions
in lattice systems with random local properties,
J. Phys. Soc. Jpn. Suppl. 26, 11–14 (1969)
22.37 C.M. Fortuin, P.W. Kasteleyn: On the random clus-
ter model. I: Introduction and relation to other
models, Physica 57,536–564(1972)
22.38 U. Wolff: Collective Monte Carlo updating for spin
systems, Phys. Rev. Lett. 62, 361–364 (1989)
22.39 P. Tamayo, R.C. Brower, W. Klein: Single-cluster
Monte-Carlo dynamics for the Ising-model, J. Stat.
Phys. 58, 1083–1094 (1990)
22.40 H.G. Evertz, G. Lana, M. Marcu: Cluster algorithm for
vertex models, Phys. Rev. Lett. 70, 875–879 (1993)
22.41 J. Machta, Y.S. Choi, A. Lucke, T. Schweizer,
L.V. Chayes: Invaded cluster algorithm for equilib-
rium critical points, Phys. Rev. Lett. 75, 2792–2795
(1995)
22.42 J. Machta, Y.S. Choi, A. Lucke, T. Schweizer,
L.V. Chayes: Invaded cluster algorithm for Potts
models, Phys. Rev. E 54, 1332–1345 (1996)
22.43 Y. Tomita, Y. Okabe: Probability-changing cluster
algorithm for Potts models, Phys. Rev. Lett. 86,
572–575 (2001)
22.44 N. Prokof’ev, B. Svistunov: Worm algorithms for
classical statistical models, Phys. Rev. Lett. 87,
160601(1–4) (2001)
Part E 22
Monte Carlo Simulation References 1151
22.45 F. Matsubara, T. Iyota, S. Inawashiro: Dynamical
simulation of the Heisenberg spin glass in three
dimensions, J. Phys. Soc. Jpn. 60, 41–44 (1991)
22.46 F. Matsubara, T. Iyota: Hybrid Monte-Carlo spin-
dynamics simulation of short-range ±J Heisenberg
models with and without anisotropy, Prog. Theor.
Phys. 90, 471–498 (1993)
22.47 S. Kirkpatrick, C.D. Gelatt, M.P. Vecchi: Optimiza-
tion by simulated annealing, Science 220,671–680
(1983)
22.48 E. Marinari, G. Parisi: Simulated tempering: A new
Monte Carlo scheme, Europhys. Lett. 19, 451–458
(1992)
22.49 W. Kerler, P. Rehberg: Simulated-tempering pro-
cedure for spin-glass simulations, Phys. Rev. E 50,
4220–4225 (1994)
22.50 K. Hukushima, K. Nemoto: Exchange Monte Carlo
method and application to spin glass simulations,
J. Phys. Soc. Jpn. 65, 1604–1608 (1996)
22.51 R.H. Swendsen, J.-S. Wang: Replica Monte Carlo
simulation of spin-glasses, Phys. Rev. Lett. 57,
2607–2609 (1986)
22.52 J.-S. Wang, R.H. Swendsen: Replica Monte Carlo
simulation (revisited), Prog. Theor. Phys. Suppl.
157, 317–323 (2005)
22.53 M. Suzuki: Quantum Monte Carlo methods in Con-
densed Matter Physics,ed.byM.Suzuki(World
Scientific, Singapore 1993)
22.54 M. Suzuki: Relationship between d-dimensional
quantal spin systems and (d+1)-dimensional Ising
systems — equivalence, critical exponents and sys-
tematic approximants of the partition function and
spin correlations, Prog. Theor. Phys. 56, 1454–1469
(1976)
22.55 M. Suzuki: Generalized Trotters formula and sys-
tematic approximants of exponential operators
and inner derivations with applications to many-
body problems, Commun. Math. Phys. 51, 183–190
(1976)
22.56 M. Suzuki: General theory of higher-order decom-
position of exponential operators and symplectic
integrators, Phys. Lett. A 165, 387–395 (1992)
22.57 M. Suzuki: General nonsymmetric higher-order
decomposition of exponential operators and sym-
plectic integrators, J. Phys. Soc. Jpn. 61,3015–3019
(1992)
22.58 J.E.Hirsch,R.L.Sugar,D.J.Scalapino,R.Blanken-
becler: Monte Carlo simulations of one-dimen-
sional fermion systems, Phys. Rev. B 26, 5033–5055
(1982)
22.59 H. De Raedt, A. Lagendijk: Monte-Carlo simulation
of quantum statistical lattice models, Phys. Rep.
127, 233–307 (1985)
22.60 M. Suzuki: Quantum Monte Carlo Methods in Equi-
librium and Nonequilibrium Systems,ed.byM.
Suzuki (Springer, Berlin Heidelberg 1987)
22.61 M. Suzuki, S. Miyashita, A. Kuroda: Monte Carlo
simulation of quantum spin systems I, Prog. Theor.
Phys. 58, 1377–1387 (1977)
22.62 T. Sakaguchi, K. Kubo, S. Takada: Monte Carlo simu-
lation for the in-plane susceptibility of 1-D spin 1/2
and 1 XY model, J. Phys. Soc. Jpn. 54, 861–864
(1985)
22.63 S. Miyashita: Thermodynamic properties of spin 1/2
antiferromagnetic Heisenberg model on the square
lattice, J. Phys. Soc. Jpn. 57, 1934–1946 (1988)
22.64 M. Suzuki: Fractal decomposition of exponential
operators with applications to many-body theories
and Monte Carlo simulations, Phys. Lett. A 146,319–
323 (1990)
22.65 M. Suzuki: General theory of fractal path inte-
grals with applications to many-body theories and
statistical physics, J. Math. Phys. 32, 400–407 (1991)
22.66 H.G. Evertz: The loop algorithm, Adv. Phys. 52,1–66
(2003)
22.67 N. Kawashima, K. Harada: Recent developments of
world-line Monte Carlo methods, J. Phys. Soc. Jpn.
73, 1379–1414 (2004)
22.68 N. Kawashima, J.E. Gubernatis: Dual Monte Carlo
and cluster algorithms, Phys. Rev. E 51, 1547–1559
(1995)
22.69 N. Kawashima, J.E. Gubernatis: Generalization of
the Fortuin–Kasteleyn transformation and its ap-
plication to quantum spin simulations, J. Stat.
Phys. 80, 169–221 (1995)
22.70 N. Kawashima: Cluster algorithms for anisotropic
quantum spin models, J. Stat. Phys. 82,131–153
(1996)
22.71 N. Kawashima, J.E. Gubernatis, H.G. Evertz: Loop
algorithms for quantum simulations of fermion
models on lattices, Phys. Rev. B 50,136–149
(1994)
22.72 B.B. Beard, U.-J. Wiese: Simulations of discrete
quantum systems in continuous Euclidean time,
Phys. Rev. Lett. 77, 5130–5133 (1996)
22.73 N. Kawashima, J.E. Gubernatis: Loop algorithms for
Monte Carlo simulations of quantum spin systems,
Phys. Rev. Lett. 73, 1295–1298 (1994)
22.74 S. Todo, K. Kato: Cluster algorithms for general-
S quantum spin systems, Phys. Rev. Lett. 87,
047203(1–4) (2001)
22.75 V.A. Kashurnikov, N.V. Prokofev, B.V. Svistunov,
M. Troyer: Quantum spin chains in a magnetic field,
Phys. Rev. B 59, 1162–1167 (1999)
22.76 N.V. Prokov’ev, B.V. Svistunov, I.S. Tupitsyn: Exact,
complete, and universal continuous-time world-
line Monte Carlo approach to the statistics of
discrete quantum systems, Sov. Phys. JETP 87,310–
321 (1998)
22.77 N.V. Prokof’ev, B.V. Svistunov, I.S. Tupitsyn:
“Worm” algorithm in quantum Monte Carlo simu-
lations, Phys. Lett. A 238, 253–257 (1998)
Part E 22
1152 Part E Modeling and Simulation Methods
22.78 O.F. Syljuåsen, A.W. Sandvik: Quantum Monte Carlo
with directed loops, Phys. Rev. E 66, 046701(1–28)
(2002)
22.79 A.W. Sandvik, J. Kurkijärvi: Quantum Monte Carlo
simulation method for spin systems, Phys. Rev. B
43, 5950–5961 (1991)
22.80 A.W. Sandvik: Generalization of Handscomb’s
quantum Monte-Carlo scheme – Application to
the 1-D Hubbard-model, J. Phys. A 25, 3667–3682
(1992)
22.81 A.W. Sandvik: Finite-size scaling of the ground-
state parameters of the two-dimensional Heisen-
berg model, Phys. Rev. B 56, 11678–11690 (1997)
22.82 A.W. Sandvik: Stochastic series expansion method
with operator-loop update, Phys. Rev. B 59,
R14157–R14160 (1999)
22.83 J.E. Hirsch: Monte Carlo study of the two-
dimensional Hubbard model, Phys. Rev. Lett. 51,
1900–1903 (1983)
22.84 J.E. Hirsch: Two-dimensional Hubbard model:
numerical simulation study, Phys. Rev. B 31, 4403–
4419 (1985)
22.85 S.R. White, D.J. Scalapino, R.L. Sugar, E.Y. Loh,
J.E. Gubernatis, R.T. Scalettar: Numerical study of
the two-dimensional Hubbard model, Phys. Rev.
B 40, 506–516 (1989)
22.86 M. Imada, Y. Hatsugai: Numerical studies on the
Hubbard model and the t-J model in one- and
two-dimensions, J. Phys. Soc. Jpn. 58,3752–3780
(1989)
22.87 J.E. Hirsch: Discrete Hubbard-Stratonovich trans-
formation for fermion lattice models, Phys. Rev. B
28, 4059–4061 (1983)
22.88 J. Kuti: Stochastic method for the numerical study
of lattice fermions, Phys. Rev. Lett. 49, 183–186
(1982)
22.89 R. Blankenbecler, R.L. Sugar: Projector Monte Carlo
method, Phys. Rev. D 27, 1304–1311 (1983)
22.90 Y.C. Chen, T.K. Lee: t-J model studied by the power
Lanczos method, Phys. Rev. B 51, 6723–6726 (1995)
22.91 S. Sorella: Green function Monte Carlo with
stochastic reconfiguration, Phys. Rev. Lett. 80,
4558–4561 (1998)
22.92 S. Sorella, L. Capriotti: Phys. Rev. B 61, 2599–2612
(2000)
22.93 S. Sorella: Generalized Lanczos algorithm for vari-
ational quantum Monte Carlo, Phys. Rev. B 64,
024512(1–16) (2001)
22.94 H.J.M. van Bemmel, D.F.B. ten Haaf, W. van
Saarloos, J.M.J. van Leeuwen, G. An: Fixed-node
quantum Monte Carlo method for lattice fermions,
Phys. Rev. Lett. 72, 2442–2445 (1994)
22.95 D.F.B. ten Haaf, H.J.M. van Bemmel, J.M.J. van
Leeuwen, W. van Saarloos, D.M. Ceperley: Proof
for an upper bound in fixed-node Monte Carlo
for lattice fermions, Phys. Rev. B 51, 13039–13045
(1995)
22.96 D.M. Ceperley, B.J. Alder: Ground state of the elec-
tron gas by a stochastic method, Phys. Rev. Lett.
45, 566–569 (1980)
22.97 D.M. Ceperley, B.J. Alder: Quantum Monte-Carlo,
Science 231, 555–560 (1986)
22.98 T. Nakamura: Vanishing of the negative-sign
problem of quantum Monte Carlo simulations in
one-dimensional frustrated spin systems, Phys.
Rev. B 57, R3197–R3200 (1998)
22.99 S. Chandrasekharan, U.-J. Wiese: Meron-cluster
solution of fermion sign problems, Phys. Rev. Lett.
83, 3116–3119 (1999)
22.100 S. Chandrasekharan, J. Cox, J.C. Osborn, U.-
J. Wiese: Meron-cluster approach to systems of
strongly correlated electrons, Nucl. Phys. B 673,
405–436 (2003)
22.101 C. Domb, M.S. Green: Phase Transitions and Critical
Phenomena, Vol. 3, ed. by C. Domb, M.S. Green
(Academic, London 1974)
22.102 G.A. Baker Jr. (Ed.): Quantitative Theory of Critical
Phenomena (Academic, San Diego 1990)
22.103 S.R. White: Density matrix formulation for quan-
tum renormalization groups, Phys. Rev. Lett. 69,
2863–2866 (1992)
22.104 S.R. White: Density-matrix algorithms for quantum
renormalization groups, Phys. Rev. B 48,10345–
10356 (1993)
22.105 T. Nishino: Density matrix renormalization group
method for 2-D classical models, J. Phys. Soc. Jpn.
64, 3598–3601 (1995)
22.106 R.J. Bursill, T. Xiang, G.A. Gehring: The density
matrix renormalization group for a quantum spin
chain at non-zero temperature, J. Phys.: Condens.
Matter 8, L583–L590 (1996)
22.107 N. Shibata: Thermodynamics of the anisotropic
Heisenberg chain calculated by the density ma-
trix renormalization group method, J. Phys. Soc.
Jpn. 66, 2221–2223 (1997)
22.108 X. Wang, T. Xiang: Transfer-matrix density-matrix
renormalization-group theory for thermodynamics
of one-dimensional quantum systems, Phys. Rev.
B 56, 5061–5064 (1997)
22.109 K. Maisinger, U. Schollwöck: Thermodynamics of
frustrated quantum spin chains, Phys. Rev. Lett.
81, 445–448 (1998)
22.110 M. Imada, T. Kashima: Path-integral renormaliza-
tion group method for numerical study of strongly
correlated electron systems, J. Phys. Soc. Jpn. 69,
2723–2726 (2000)
22.111 T. Kashima, M. Imada: Path-integral renor-
malization group method for numerical study
on ground states of strongly correlated elec-
tronic systems, J. Phys. Soc. Jpn. 70, 2287–2299
(2001)
22.112 M. Imada, T. Mizusaki: Quantum-number projec-
tion in the path-integral renormalization group
method, Phys. Rev. B 69, 125110–1–125110–10 (2004)
Part E 22
Monte Carlo Simulation References 1153
22.113 T. Kashima, M. Imada: Magnetic and metal-
insulator transitions through bandwidth control
in two-dimensional Hubbard models with near-
est and next-nearest neighbor transfers, J. Phys.
Soc. Jpn. 70, 3052–3067 (2001)
22.114 H. Morita, S. Watanabe, M. Imada: Nonmagnetic
insulating states near the Mott transitions on lat-
tices with geometrical frustration and implications
for κ-(ET)
2
Cu
2
(CN)
3
, J. Phys. Soc. Jpn. 71, 2109–2112
(2002)
22.115 S. Watanabe, M. Imada: Precise determination
of phase diagram for two-dimensional Hubbard
model with filling- and bandwidth-control Mott
transitions: grand-canonical path-integral renor-
malization group approach, J. Phys. Soc. Jpn. 73,
1251–1266 (2004)
22.116 S.-C. Zhang: A unified theory based on SO(5)
symmetry of superconductivity and antiferromag-
netism, Science 275, 1089–1096 (1997)
22.117 E. Demler, W. Hanke, S.-C. Zhang: SO(5) theory
of antiferromagnetism and superconductivity, Rev.
Mod. Phys. 76,909–974(2004)
22.118 K.-S. Liu, M.E. Fisher, D.R. Nelson: Quantum lattice
gas and the existence of a supersolid, J. Low. Temp.
Phys. 10, 655–683 (1973)
22.119 M.E. Fisher, D.R. Nelson: Spin flop, supersolids, and
bicritical and tetracritical points, Phys. Rev. Lett.
32,1350–1353(1974)
22.120 D.R. Nelson, J.M. Kosterlitz, M.E. Fisher: Re-
normalization-group analysis of bicritical and
tetracritical points, Phys. Rev. Lett. 33, 813–817
(1974)
22.121 D.R. Nelson, M.E. Fisher, J.M. Kosterlitz: Bicritical
and tetracritical points in anisotropic antifer-
romagnetic systems, Phys. Rev. B 13,412–432
(1976)
22.122 A. Aharony: Comment on “Bicritical and tetracriti-
cal phenomena and scaling properties of the SO(5)
theory”, Phys. Rev. Lett. 88, 059703(1) (2002), and
references therein
22.123 X. Hu: Bicritical and tetracritical phenomena and
scaling properties of the SO(5) theory, Phys. Rev.
Lett. 87 (2001)
22.124 X. Hu: Bicritical phenomena and scaling properties
of O(5) model, Physica A 321, 71–80 (2003)
22.125 E. Arrigoni, W. Hanke: Renormalized SO(5) sym-
metry in ladders with next-nearest-neighbor
hopping, Phys. Rev. Lett. 82, 2115–2118 (1999)
22.126 E. Arrigoni, W. Hanke: Critical properties of pro-
jected SO(5) models at finite temperatures, Phys.
Rev. B 62, 11770–11777 (2000)
22.127 X. Hu: Reply to “Comment on ‘Bicritical and tetra-
critical phenomena and scaling properties of the
SO(5) theory’”, Phys. Rev. Lett. 88, 059704(1–4)
(2002)
22.128 P. Pfeuty, D. Jasnow, M.E. Fisher: Crossover scaling
functions for exchange anisotropy, Phys. Rev. B 10,
2088–2112 (1974)
22.129 X.Hu,T.Koyama,M.Tachiki:Phasediagramof
a superconducting and antiferromagnetic system
with SO(5) symmetry, Phys. Rev. Lett. 82,2568–2571
(1999)
22.130 A.A. Abrikosov: On the magnetic properties of su-
perconductors of the second group, Zh. Eksp. Teor.
Fiz. 32, 1442 (1957)
22.131 A.A. Abrikosov: On the magnetic properties of su-
perconductors of the second group, Sov. Phys. JETP
5, 1174–1182 (1957)
22.132 G. Blatter, M.V. Feigelman, V.B. Geshkenbein,
A.I. Larkin, V.M. Vinokur: Vortices in high-
temperature superconductors, Rev. Mod. Phys. 66,
1125–1388 (1994)
22.133 G.W. Crabtree, D.R. Nelson: Vortex physics in high-
temperature superconductors, Phys. Today 50,38–
45 (1997)
22.134 T. Nattermann, S. Scheidl: Vortex-glass phases in
type-II superconductors, Adv. Phys. 49,607–704
(2000)
22.135 E. Brezin, D.R. Nelson, A. Thiaville: Fluctuation ef-
fects near H
c2
in type-II superconductors, Phys.
Rev. B 31,7124–7132(1985)
22.136 Y.-H. Li, S. Teitel: Vortex-line-lattice melting,
vortex-line cutting, and entanglement in model
high-T
c
superconductors, Phys. Rev. Lett. 66,
3301–3304 (1991)
22.137 R.E. Hetzel, A. Sudb, D.A. Huse: First-order melting
transition of an Abrikosov vortex lattice, Phys. Rev.
Lett. 69, 518–521 (1992)
22.138 P.G. de Gennes: Superconductivity of Metals and
Alloys (Addison-Wesley, Redwood City, CA 1966),
translated by P.A. Pincus
22.139 W.E. Lawrence, S. Doniach: Proceedings of LT12,
Tokyo, 1970, ed. by E. Kanda (Keigaku, Tokyo 1971)
22.140 X. Hu, S. Miyashita, M. Tachiki: Simulation for
the first-order vortex-lattice melting transition
in high-T
c
superconductors, Physica (Amsterdam)
282-287C, 2057–2058 (1997)
22.141 X.Hu,S.Miyashita,M.Tachiki:δ-function peak
in the specific heat of high-T
c
superconductors:
Monte Carlo simulation, Phys. Rev. Lett. 79,3498–
3501 (1997)
22.142 X.Hu,S.Miyashita,M.Tachiki:MonteCarlosimu-
lation on the first-order melting transition of
high-T
c
superconductors in
ˆ
c, Phys. Rev. B 58,
3438–3445 (1998)
22.143 S. Miyashita, H. Nishimori, A. Kuroda, M. Suzuki:
Monte Carlo simulation and static and dynamic
critical behavior of the plane rotator model, Prog.
Theo. Phys. 60, 1669–1685 (1978)
22.144 A.E. Koshelev: Point-like and line-like melting of
the vortex lattice in the universal phase diagram
of layered superconductors, Phys. Rev. B 56, 11201–
11212 (1997)
22.145 A.K. Nguyen, A. Sudbø: Phase coherence and the
boson analogy of vortex liquids, Phys. Rev. B 58,
2802–2815 (1998)
Part E 22
1154 Part E Modeling and Simulation Methods
22.146 P. Olsson, S. Teitel: Correlation lengths in the vortex
line liquid of a high-T
c
superconductor, Phys. Rev.
Lett. 82, 2183–2186 (1999)
22.147 X. Hu, M. Tachiki: Possible tricritical point in phase
diagrams of interlayer josephson-vortex systems
in high-T
c
superconductors, Phys. Rev. Lett. 85,
2577–2580 (2000)
22.148 K.B. Efetov: Fluctuations in layered superconduc-
tors in a parallel magnetic field, Sov. Phys. JETP 49,
905–910 (1979)
22.149 B.I. Ivlev, N.B. Kopnin, M.M. Slomaa: Vortex-
lattice/vortex-liquid states in anisotropic high-T
c
superconductor, Phys. Rev. B 43, 2896–2902 (1991)
22.150 B.I. Ivlev, N.B. Kopnin, V.L. Pokrovsky: Shear insta-
bility of a vortex lattice in layered superconductors,
J. Low. Temp. Phys. 80, 187 (1990)
22.151 L.V. Mikheev, E.B. Kolomeisky: Melting of a flux-
line fluid confined by CuO
2
planes: Lindemann-
criterion failure, Phys. Rev. B 43, 10431–10435
(1991)
22.152 S.E. Korshunov, A.I. Larkin: Problem of Josephson-
vortex-lattice melting in layered superconductors,
Phys. Rev. B 46, 6395–6399 (1992)
22.153 G. Blatte, B.I. Ivlev, J. Rhyner: Kosterlitz–Thouless
transition in the smectic vortex state of a layered
superconductor, Phys. Rev. Lett. 66, 2392–2395
(1991)
22.154 L. Balents, D.R. Nelson: Fluctuations and intrin-
sic pinning in layered superconductors, Phys. Rev.
Lett. 73, 2618–2621 (1994)
22.155 L. Balents, D.R. Nelson: Quantum smectic and su-
persolid order in helium films and vortex arrays,
Phys. Rev. B 52, 12951–12968 (1995)
22.156 Y. Iye, S. Nakamura, T. Tamegai: Absence of current
direction dependence of the resistive state of high
temperature superconductors in magnetic fields,
Physica 159C, 433–438 (1989)
22.157 W.K. Kwok, U. Welp, G.W. Crabtree, K.G. Van-
dervoort, R. Hulscher, J.Z. Liu: Direct observation
of dissipative flux motion and pinning by twin
boundaries in YBa
2
Cu
3
O
7−δ
single crystals, Phys.
Rev. Lett. 64, 966–969 (1990)
22.158 W.K. Kwok, J. Fendrich, U. Welp, S. Fleshler,
J. Downey, G.W. Crabtree: Suppression of the first
order vortex melting transition by intrinsic pin-
ning in YBa
2
Cu
3
O
7−δ
, Phys. Rev. Lett. 72, 1088–1091
(1994)
22.159 X. Hu, M. Tachiki: Decoupled two-dimensional
superconductivity and continuous melting tran-
sitions in layered superconductors immersed in
a parallel magnetic field, Phys. Rev. B 70,
064506(1–13) (2004)
22.160 X. Hu, M. Tachiki: Structure and phase transition of
josephson vortices in anisotropic high-T
c
super-
conductors, Phys. Rev. Lett. 80, 4044–4047 (1998)
22.161 X. Hu: Pinning effects in vortex states of high-T
c
superconductors: Monte Carlo simulations, J. Low.
Temp. Phys. 131, 979–986 (2003)
22.162 X. Hu, M.-B. Luo, Y.-Q. Ma: Density functional the-
ory for freezing transition of vortex-line liquid with
periodic layer pinning, Phys. Rev. B 72,174503(1–6)
(2005)
22.163 A.I. Larkin: Effect of inhomogeneities on the struc-
ture of the mixed state of superconductors, Sov.
Phys. JETP 31, 784–786 (1970)
22.164 A.I. Larkin, Y.N. Ovchinnikov: Pinning in type II su-
perconductors, J. Low. Temp. Phys. 34,409–428
(1979)
22.165 Y. Imry, S.-K. Ma: Random-field instability of the
ordered state of continuous symmetry, Phys. Rev.
Lett. 35, 1399–1401 (1975)
22.166 T. Nattermann: Scaling approach to pinning:
Charge density waves and giant flux creep in
superconductors, Phys. Rev. Lett. 64, 2454–2457
(1990)
22.167 S.E. Korshunov: Replica symmetry breaking in vor-
tex glasses, Phys. Rev. B 48, 3969–3975 (1993)
22.168 T. Giamarchi, P. Le Doussal: Elastic theory of pinned
flux lattices, Phys. Rev. Lett. 72, 1530–1533 (1994)
22.169 T. Giamarchi, P. Le Doussal: Elastic theory of flux
lattices in the presence of weak disorder, Phys.
Rev. B 52, 1242–1270 (1995)
22.170 T. Giamarchi, P. Le Doussal: Phase diagrams of flux
lattices with disorder, Phys. Rev. B 55, 6577–6583
(1997)
22.171 P. Olsson, S. Teitel: Disorder driven melting of the
vortex line lattice, Phys. Rev. Lett. 87, 137001(1–4)
(2001)
22.172 Y. Nonomura, X. Hu: Effects of point defects on the
phase diagram of vortex states in high-T
c
super-
conductors in the B c cxis, Phys. Rev. Lett. 86,
5140–5143 (2001)
22.173 Y. Nonomura, X. Hu: Crossover behaviors in liquid
region of vortex states above a critical point caused
by point defects, cond-mat/0302597
22.174 Y. Nonomura, X. Hu: Possible Bragg–Bose glass
phase in vortex states of high-T
c
superconductors
with sparse and weak columnar defects, Europhys.
Lett. 65, 533–539 (2004)
22.175 M.J.P. Gingras, D.A. Huse: Topological defects in
the random-field XY model and the pinned vortex
lattice to vortex glass transition in type-II super-
conductors, Phys. Rev. B 53, 15193–15200 (1996)
22.176 S. Ryu, A. Kapitulnik, S. Doniach: Field-driven
topological glass transition in a model flux line
lattice, Phys. Rev. Lett. 77, 2300–2303 (1996)
22.177 M.P.A. Fisher: Vortex-glass superconductivity:
A possible new phase in bulk high-T
c
oxides, Phys.
Rev. Lett. 62, 1415–1418 (1989)
22.178 M.P.A. Fisher, D.S. Fisher, D.A. Huse: Thermal fluc-
tuations, quenched disorder, phase transitions,
and transport in type-II superconductors, Phys.
Rev. B 43, 130–159 (1991)
22.179 A. van Otterlo, R.T. Scalettar: Phase diagram of
disordered vortices from London Langevin simu-
lations, Phys. Rev. Lett. 81, 1497–1500 (1998)
Part E 22
Monte Carlo Simulation References 1155
22.180 R. Sugano, T. Onogi, K. Hirata, M. Tachiki: The effect
of pointlike pinning on vortex phase diagram of
Bi
2
Sr
2
CaCu
2
O
8+δ
, Physica C 357-360, 428–431 (2001),
and references therein
22.181 A. Vestergren, J. Lidmar, M. Wallin: Vortex glass
transition in a random pinning model, Phys. Rev.
Lett. 88, 117004(1–4) (2002)
22.182 P. Olsson: Vortex glass transition in a frustrated
3-D XY model with disorder, Phys. Rev. Lett. 91,
077002(1–4) (2003)
22.183 J. Lidmar: Amorphous vortex glass phase in
strongly disordered superconductors, Phys. Rev.
Lett. 91, 097001(1–4) (2003)
22.184 F.O. Pfeiffer, H. Rieger: Numerical study of
the strongly screened vortex-glass model in
an external field, Phys. Rev. B 60,6304–6307
(1999)
22.185 H. Kawamura: Simulation studies on the stability
of the vortex-glass order, J. Phys. Soc. Jpn. 69,
29–32 (2000)
22.186 T.K. Worthington, M.P.A. Fisher, D.A. Huse, J. Toner,
A.D. Marwick, T. Zabel, C.A. Feild, F. Holtzberg:
Phys. Rev. B 46, 11854–11861 (1992)
22.187 T. Nishizaki, K. Shibata, T. Sasaki, N. Kobayashi:
New equilibrium phase diagram of YBa
2
Cu
3
O
y
under high magnetic fields, Physica C 341-348,
957–960 (2000)
22.188 K. Shibata, T. Nishizaki, T. Sasaki, N. Kobayashi:
Phase transition in the vortex liquid and the critical
endpoint in YBa
2
Cu
3
O
y
, Phys. Rev. B 66, 214518(1–7)
(2002)
22.189 J. Kierfeld, V. Vinokur: Dislocations and the critical
endpoint of the melting line of vortex line lattices,
Phys. Rev. B 61, R14928–14931 (2000)
22.190 G.P. Mikitik, E.H. Brandt: Effect of pinning on the
vortex-lattice melting line in type-II superconduc-
tors, Phys. Rev. B 68, 054509(1–15) (2003)
22.191 F. Bouquet, C. Marcenat, E. Steep, R. Calemczuk,
W.K. Kwok, U. Welp, G.W. Crabtree, R.A. Fisher,
N.E. Phillips, A. Schilling: An unusual phase tran-
sition to a second liquid vortex phase in the
superconductor YBa
2
Cu
3
O
7
,Nature411, 448–451
(2001)
22.192 M.P.A. Fisher, P.B. Weichman, G. Grinstein,
D.S. Fisher: Boson localization and the superfluid-
insulator transition, Phys. Rev. B 40,546–570
(1989)
22.193 D.R. Nelson, V.M. Vinokur: Boson localization
and pinning by correlated disorder in high-
temperature superconductors, Phys. Rev. Lett. 68,
2398–2401 (1992)
22.194 D.R. Nelson, V.M. Vinokur: Boson localization and
correlated pinning of superconducting vortex ar-
rays, Phys. Rev. B 48, 13060–13097 (1993)
22.195 J. Lidmar, M. Wallin: Critical properties of Bose-
glass superconductors, Europhys. Lett. 47,494–500
(1999)
22.196 L. Radzihovsky: Resurrection of the melting line in
the Bose glass superconductor, Phys. Rev. Lett. 74,
4923–4926 (1995)
22.197 T. Giamarchi, P. Le Doussal: Variational theory of
elastic manifolds with correlated disorder and lo-
calization of interacting quantum particles, Phys.
Rev. B 53, 15206–15225 (1996)
22.198 C. Zeng, P.L. Leath, D.S. Fisher: Absence of two-
dimensional Bragg glasses, Phys. Rev. Lett. 82,
1935–1938 (1999)
22.199 S. Tyagi, Y.Y. Goldschmidt: Effects of columnar dis-
order on flux-lattice melting in high-temperature
superconductors, Phys. Rev. B 67, 214501(1–15)
(2003)
22.200 C. Dasgupta, O.T. Valls: Two-step melting of the
vortex solid in layered superconductors with ran-
dom columnar pins, Phys. Rev. Lett. 91, 127002(1–4)
(2003)
22.201 C. Dasgupta, O.T. Valls: Melting and structure of the
vortex solid in strongly anisotropic layered super-
conductors with random columnar pins, Phys. Rev.
B 69, 214520(1–16) (2004)
22.202 M. Kohno, M. Takahashi, M. Hagiwara: Low-
temperature properties of the spin-1 antiferro-
magnetic Heisenberg chain with bond alternation,
Phys. Rev. B 57, 1046–1051 (1998)
22.203 F.D.M. Haldane: Nonlinear field theory of large-
spin Heisenberg antiferromagnets: semiclassically
quantized solitons of the one-dimensional easy-
axis Néel state, Phys. Rev. Lett. 50, 1153–1156 (1983)
22.204 F.D.M. Haldane: Continuum dynamics of the 1-D
Heisenberg antiferromagnet: identification with
the O(3) nonlinear sigma model, Phys. Lett. A 93,
464–468 (1983)
22.205 M.P. Nightingale, H.W. Blöte: Gap of the linear
spin-1 Heisenberg antiferromagnet: a Monte Carlo
calculation, Phys. Rev. B 33, 659–661 (1986)
22.206 M. Takahashi: Spin-correlation function of the S =1
antiferromagnetic Heisenberg chain at T =0, Phys.
Rev. B 38, 5188–5191 (1988)
22.207 Y. Kato, A. Tanaka: Numerical study of the S =1an-
tiferromagnetic spin chain with bond alternation,
J. Phys. Soc. Jpn. 63, 1277–1280 (1994)
22.208 W.J.L. Buyers, R.M. Morra, R.L. Armstrong,
M.J. Hogan, P. Gerlach, K. Hirakawa: Experimen-
tal evidence for the Haldane gap in a spin-1 nearly
isotropic, antiferromagnetic chain, Phys. Rev. Lett.
56, 371–374 (1986)
22.209 M. Steiner, K. Kakurai, J.K. Kjems, D. Petitgrand,
R. Pynn: Inelastic neutron scattering studies on 1-D
near-Heisenberg antiferromagnets: A test of the
Haldane conjecture, J. Appl. Phys. 61, 3953–3955
(1987)
22.210 I.A. Zaliznyak, L.P. Regnault, D. Petitgrand:
Neutron-scattering study of the dynamic spin cor-
relations in CsNiCl
3
above Néel ordering, Phys. Rev.
B 50, 15824–15833 (1994)
Part E 22
1156 Part E Modeling and Simulation Methods
22.211 J.P. Renard, M. Verdaguer, L.P. Regnault,
W.A.C. Erkelens, J. Rossat-Mignod, W.G. Stir-
ling: Presumption for a quantum energy-gap
in the quasi one-dimensional S =1 Heisenberg-
antiferromagnet Ni(C
2
H
8
N
2
)
2
NO
2
(ClO
4
), Europhys.
Lett. 3,945–951(1987)
22.212 I. Affleck: The quantum Hall-effects, σ -models at
θ = π and quantum spin chains, Nucl. Phys. B 257,
397–406 (1985)
22.213 I. Affleck: Exact critical exponents for quantum
spin chains, nonlinear σ -models at θ =π and the
quantum Hall-effect, Nucl. Phys. B 265, 409–447
(1986)
22.214 I. Affleck, F.D.M. Haldane: Critical theory of quan-
tumspinchains,Phys.Rev.B36,5291–5300
(1987)
22.215 E. Coronado, M. Drillon, A. Fuertes, D. Beltran,
A. Mosset, J. Galy: Structural and magnetic study
of Ni
2
(EDTA)(H
2
O)
4
,2H
2
O - alternating Landé factors
in a two-sublattice 1-D system, J. Am. Chem. Soc.
108, 900–905 (1986)
22.216 R.Vicente,A.Escuer,J.Ribas,X.Solans:Thefirst
nickel(II) alternating chain with two different end-
to-end azido bridges, Inorg. Chem. 31,1726–1728
(1992)
22.217 A. Escuer, R. Vicente, J. Ribas, M.S.E. Fallah,
X. Solans, M. Font-Badría: Crystal structure and
magnetic properties of trans-[Ni(333-tet)(μ-N
3
)]
n
(ClO
4
)
n
and cis-[Ni(333-tet)(μ-(N
3
))]
n
(PF
6
)
n
:two
novel kinds of structural nickel(II) chains with
a single azido bridge. Magnetic behavior of an al-
ternating S = 1chainwithα =0.46, Inorg. Chem.
33, 1842–1847 (1994)
22.218 J.J. Borrás-Almenar, E. Coronado, J. Curely,
R. Georges: Exchange alternation and single-ion
anisotropy in the antiferromagnetic Heisenberg
chain S =1. Magnetic and thermal properties of
the compound Ni
2
(EDTA)·6H
2
O, Inorg. Chem. 34,
2699–2704 (1995)
22.219 A. Escuer, R. Vicente, X. Solans, M. Font-Badría:
Crystal structure and magnetic properties of
[Ni
2
(dpt)
2
(μ-ox)(μ-N
3
)
n
](PF
6
)
n
:anewstrategyto
obtain S =1 alternating chains, Inorg. Chem. 33,
6007–6011 (1994)
22.220 M. Hagiwara, Y. Narumi, K. Kindo, M. Kohno,
H. Nakano, R. Sata, M. Takahashi: Experimental
verification of the gapless point in the S =1an-
tiferromagnetic bond alternating chain, Phys. Rev.
Lett. 80, 1312–1315 (1998)
22.221 O.A. Starykh, R.R.P. Singh, A.W. Sandvik: Quantum
critical scaling and temperature-dependent log-
arithmic corrections in the spin-half Heisenberg
chain, Phys. Rev. Lett. 78, 539–542 (1997)
22.222 O.A. Starykh, A.W. Sandvik, R.R.P. Singh: Dynamics
of the spin-1/2 Heisenberg chain at intermedi-
ate temperatures, Phys. Rev. B 55, 14953–14967
(1997)
22.223 N. Furukawa, M. Imada: Two-dimensional Hub-
bard model – metal insulator transition studied
by Monte Carlo calculation, J. Phys. Soc. Jpn. 61,
3331–3354 (1992)
22.224 A. Ino, T. Mizokawa, A. Fujimori, K. Tamasaku,
H. Eisaki, S. Uchida, T. Kimura, T. Sasagawa,
K. Kishio: Chemical potential shift in overdoped
and underdoped La
2−x
Sr
x
CuO_4, Phys. Rev. Lett.
79, 2101–2104 (1997)
22.225 N. Harima, A. Fujimori, T. Sugaya, I. Terasaki:
Chemical potential shift in lightly doped to over-
doped Bi
2
Sr
2
Ca
1−x
R
x
Cu
2
O
8+y
(R=Pr, Er), Phys. Rev.
B 67, 172501(1–4) (2003)
22.226 R.J. Birgeneau, D.R. Gabbe, H.P. Jenssen,
M.A. Kastner, P.J. Picone, T.R. Thurston, G. Shirane,
Y. Endoh, M. Sato, K. Yamada, Y. Hidaka, M. Oda,
Y. Enomoto, M. Suzuki, T. Murakami: Antiferro-
magnetic spin correlations in insulating, metallic,
and superconducting La
2−x
Sr
x
CuO
4
, Phys. Rev. B
38, 6614–6623 (1988)
22.227 M. Kohno: Ground-state properties of the two-
dimensional t-J model, Phys. Rev. B 55, 1435–1441
(1997)
22.228 M. Kohno, M. Takahashi: Magnetization process
of the spin-1/2 XXZ models on square and cubic
lattices, Phys. Rev. B 56, 3212–3217 (1997)
22.229 V.J. Emery, S.A. Kivelson, H.Q. Lin: Phase separa-
tion in the t-J model, Phys. Rev. Lett. 64, 475–478
(1990)
22.230 W.O. Putikka, M.U. Luchini, T.M. Rice: Aspects of the
phase diagram of the two-dimensional t-J model,
Phys. Rev. Lett. 68, 538–541 (1992)
22.231 W.O. Putikka, M.U. Luchini: Limits on phase sep-
aration for two-dimensional strongly correlated
electrons, Phys. Rev. B 62, 1684–1687 (2000)
22.232 P. Prelov
ˇ
sek, X. Zotos: Hole pairing and clustering
in the two-dimensional t-J model, Phys. Rev. B
47, 5984–5991 (1993)
22.233 E. Dagotto, J. Riera, Y.C. Chen, A. Moreo,
A. Nazarenko, F. Alcaraz, F. Ortolani: Supercon-
ductivity near phase separation in models of
correlated electrons, Phys. Rev. B 49,3548–3565
(1994)
22.234 J. Jakli
ˇ
c, P. Prelov
ˇ
sek: Thermodynamic properties of
the planar t-J model, Phys. Rev. Lett. 77, 892–895
(1996)
22.235 C.S. Hellberg, E. Manousakis: Phase separation at
all interaction strengths in the t-J model, Phys.
Rev. Lett. 78, 4609–4612 (1997)
22.236 C.S. Hellberg, E. Manousakis: Green’s-function
Monte Carlo for lattice fermions: application to
the t-J model, Phys. Rev. B 61, 11787–11806
(2000)
22.237 S.R. White, D.J. Scalapino: Density matrix renor-
malization group study of the striped phase in
the 2-D t-J model, Phys. Rev. Lett. 81, 1272–1275
(1998)
Part E 22
Monte Carlo Simulation References 1157
22.238 S.R. White, D.J. Scalapino: Energetics of domain
walls in the 2-D t-J model, Phys. Rev. Lett. 81,
3227–3230 (1998)
22.239 C.T. Shih, Y.C. Chen, T.K. Lee: Revisit phase sepa-
ration of the two-dimensional t-J model by the
power-Lanczos method, J. Phys. Chem. Sol. 62,
1797–1811 (2001)
22.240 J.D. Cloizeaux, M. Gaudin: Anisotropic linear mag-
netic chain, J. Math. Phys. (N.Y.) 7,1384–1400
(1966)
Part E 22