LARGE-SCALE SIMULATIONS OF PHASE TRANSITIONS AND LOW-DIMENSIONAL MAGNETS
I n s t i t u t e of Physics, A d a m Mickiewicz University
u l . U m u l t o w s k a 85, 61-614 Poznań, P o l a n d
e-mail: g j k @ p e a r l . a m u . e d u . p l
DOI: 10.12921/cmst.1996.01.01.55-98
OAI: oai:lib.psnc.pl:469
Abstract:
Recent developments in computer simulations of phase transitions in Ising-like systems and thermodynamic behaviour of quantum spin chains are reviewed. A combination of stochastic Monte Carlo as well as deterministic transfer matrix and finite-size diagonalization methods is described in both fields as regards static properties. Asymptotic analysis and extrapolation techniques are presented in detail. Some effective-field methods, series expansions, spin dynamics simulations and experimental applications are also discussed.
References:
Achiwa, N. (1969) Linear antiferromagnetic chains in hexagonal ABCl3-type compounds (A; Cs or Rb, B;Cu, Ni, Co or Fe). J. Phys. Soc. Jpn., 27, 561
Aharony, A. and M.E. Fisher (1983) Nonlinear scaling fields and corrections to scaling near criticality. Phys. Rev., B27, 4394
Allroth, E. and H.J. Mikeska (1981) Solitons and magnons in sine-Gordon like magnets. Z. Phys., B43, 209
Baillie, C.F., R. Gupta, K.A. Hawick and G.S. Pawley (1992) Monte Carlo renormalization
group studies of the three-dimensional Ising model. Phys. Rev., B45, 10438
Barber, M.N. (1983) Finite-Size Scaling. In C. Domb and J.L. Lebowitz (Eds.),
Phase Transitions and Critical Phenomena, Vol.8, Academic Press, London
Baxter, R.J. (1982) Exactly Solvable Models in Statistical Mechanics. Academic
Press, New York
Baxter^ R.J., I.G. Enting and S.K. Tsang (1980) Hard-square lattice gas. J. Stat.
Phys., 22, 465
Binder, K. (1981) Finite size scaling analysis of Ising model block distribution
functions. Z. Phys., B43, 119
Blöte, H. (1975) The specific heat of magnetic linear chains. Physica, B79, 427
Blöte, H., A. Compa.gner and A. Hoogland (1987) The simple quadratic Ising
model with crossing bonds. Physica, A141, 375
Blöte, H. and G. Kamieniarz (1993) Finite-size calculations of the three-dimensional
Ising model. Physica, A196, 455
Blöte, H. and G. Kamieniarz (1994) Simulations of the 3D Ising model at criticality.
Acta Phys. Polon., A85, 389
Blöte, H. and X.N. Wu (1990) Accurate determination of the critical line of the
square Ising antiferromagnet in afield. J. Phys. A: Math. Gen., 23, L627
Bonner, J.C. and M.E. Fisher (1964) Linear magnetic chains with anisotropic
coupling. Phys. Rev., A135, 640
Bruce, A.D. (1985) Universality in the two-dimensional continuous spin model. J.
Phys. A: Math. Gen., 18, L873
Burkhardt, T.W. and B. Derrida (1985) Moments of the total magnetization and
conformal invariance in the finite two-dimensional Ising model. Phys. Rev., B32,
7273
Cachine, J., J.R. Drugovich de Feli and N. Caticha (1989) Non-universal exponents
and marginal operators via a Monte Carlo renormalisation-group. J. Phys. A:
Math. Gen.,22, 1639
R. Dekeyser, Phys. Rev. B42, 10765 (1990)
Campana, L.S., A. Caramico D’Auria, U. Esposito, G. Kamieniarz and R. Dekeyser
(1990) Specific heat of (C6HnNh3)CuBr3 and (C3HiiNH3)CuC13 within
series analysis of finite chain data. Phys. Rev., B42, 10765
Campana, L.S., A. Caramico D’Auria, F. Esposito, U. Esposito, R.W. Gerling,
and G. Kamieniarz (1992a) Static prperties of quantum spin S=1 chains: TMNB,
TMNC and CsNiF3. J. Phys.: Cond. Matter, 4, 2915
Campana L.S., A. Caramico D’Auria, F. Esposito, U. Esposito, G. Kamieniarz
(1992b) Finite-Chain approach to the study of CsNiCh- Phys. Rev., B45, 5035
Campana, L.S., A. Caramico D’Auria, F. Esposito, U. Esposito and G. Kamieniarz
(1996), Phys. Rev. B
Cardy, J.L. (1987) Conformal Invariance. In C. Domb and J.L. Lebowitz (Eds.)
Phase Transitions and Critical Phenomena Vol. 11 Academic Press, New York
Cuccoli, A., V. Tognetti, P. Verrucchi and R. Vaia (1992) Quantum thermodynamics
of the easy-plane ferromagnetic chain. Phys. Rev., B46, 11601
Cullen, J.J. and D.P. Landau (1983) Monte Carlo studies of one-dimensional quantum
Heisenberg and XY-models. Phys. Rev., B27, 297
Darriet, J. and L.P. Regnault (1993) The compound Y2BaNi05: a new example
of a Haldane-gap in S=1 magnetic chain. Solid State Commun., 86, 409
Dekeyser, R. and G. Kamieniarz (1992) Effective field methods with correlations
in magnetic systems. J. Magn. Magn. Mat., 104-107, 273
Delica, T. and H. Leschke (1990) Formulation and numerical results of the transfer-
matrix method for quantum spin chains. Physica, A168, 736
Delica, T., W.J.M. de Jonge, K. Kopinga, H. Leschke and H.J. Mikeska (1991)
Static properties of CsNiF3: Comparison of numerical results, experimental data
and predictions from soliton-bearing models. Phys. Rev., B44, 11773
Dupas, C. and J.P. Renard (1977) Low-temperature magnetic properties of three
linear S=1 ferromagnets with an easy plane anisotropy: TMNB, TMNC and
CsNiF3. J. Phys. C: Solid State Phys., 10, 5057
Ferrenberg, A.M. and D.P. Landau (1991) Critical behavior of the three-dimensional
Ising model: a high resolution Monte Carlo study. Phys. Rev., B44, 5081
Fisher, M.E. and H. Au-Yang (1979) Inhomogeneous differential approximants for
power series. J. Phys. A: Math. Gen., 12, 1677
Gadet, V., M. Verdaguer, V. Briois, A. Gleizes, J.P. Renard, P. Beauvillain, C.
Chappert, T. Goto, K. Le Dang and P. Veillet (1991) Structural and magnetic
properties of (CH3)4NNi(N02)3: a Haldane-gap system. Phys. Rev., B44, 705
Gatteschi, D., A. Caneschi, L, Pardi and R. Sessoli (1994) Large clusters of metal
ions: the transition from molecular to bulk magnets. Science, 265, 1054
Gerling, R.W. and D.P. Landau (1990) Spin dynamics study of the classical ferromagnetic
XY chain. Phys. Rev., B41, 7139
Grille, H., G. Kamieniarz and R.W. Gerling (1992) Spin dynamics of the classical
easy-plane Heisenberg chain. J. Magn. Magn. Mat., 104-107, 1067
Halperin, B.I. (1992) Quantum antiferromagnets in one and two dimensions. J.
Magn. Magn. Mat., 104-107, 761
Indekeu, J.O., A.Maritan and A.L.Stella (1982) Renormalization group recursions
by mean-field approximations. J. Phys. A: Math. Gen. 15, L291
de Jongh, L.J. and A.R. Miedema (1974) Experiments on simple magnetic model
systems. Adv. Phys., 23, 1
Kakurai, K., M. Steiner and B. Dorner (1990) Study of the spin weave linewidth in
ID easy-plane ferromagnet using neutron polarization analysis. Europhys. Lett.,
12,653
Kamieniarz, G., F. Mallezie and R. Dekeyser (1988) Magnetization and correlation
length of the easy-plane ferromagnetic chain: numerical analysis and application
to (C6HilNH3)CuBr3. Phys. Rev., B38, 6941
Kamieniarz, G. and H.W.J. Blöte (1993a) Universal ratio of magnetization moments
in two-dimensional Ising model. J. Phys. A: Math. Gen., 26, 201
Kamieniarz, G. and H. Blöte (1993b) The non-interacting hard-square lattice gas:
Ising universality. J. Phys. A: Math. Gen., 26, 6679
Kamieniarz, G., G. Musial and R. Dekeyser (1994) Effective field methods for
magnetic systems. Acta Phys. Polon., A85, 413
Kamieniarz, G. and R. Matysiak (1996a), in preparation
Kamieniarz, G., G. Musial and R. Dekeyser (1996b), in preparation
Klümper, A. and P.A. Pearce (1993) New results for exactly solvable critical RSOS
models and vertex models in two dimensions. Physica, A194, 397
Kopinga, K., J. Emmen, G.C. de Vries, L.F. Lemmens and G. Kamieniarz (1988)
Comparison between experiment and numerical calculations on S = l / 2 Heisenberg-
XY ferromagnetics chains. J. de Physique, C8, 1451
Kopinga, K., T. Delica and H. Leschke (1989) Static properties of an easy-plane
ferromagnetics S = l / 2 chain: comparison of numerical results and experimental
data on (C6HiiNH3)CuBr3. Phys. Rev., B40, 7239
Kopinga, K., T. Delica, H. Leschke and I. Riedel (1993) Static properties of a
ferromagnetic S = l / 2 chain system with orthorombic exchange anisotropy: comparison
of numerical results and experimental data on (CgITu NH3)CuCl3. Phys.
Rev., B47, 5447
Landau, D.P. (1994) Computer simulation studies of critical phenomena. Physica,
A205, 41
Le Guillou, J.C. and J. Zinn-Justin (1980) Critical exponents from field theory.
Phys. Rev., B21, 3976
Liu, A.J. and M.E. Fisher (1989) The three-dimensional Ising model revisited
numerically. Physica, A156, 35
Livet, F. (1991) The cluster updating Monte Carlo algorithm applied to the 3D
Ising problem. Europhys. Lett., 16, 139
Heisenberg antiferromagnet on a square lattice
and its applications to the cuprous oxides. Rev. Mod. Phys., 63, 1
Mikeska, H.J. (1978) Solitons in a one-dimensional magnet with an easy plane. J.
Phys. G: Solid State Phys., 11, L29
Manousakis, E. (1991) The spinMikeska,
H.J. and M. Steiner (1991) Solitary excitations in one-dimensional magnets.
Adv. Phys., 40, 191
Morra, R.M., R.M. Armstrong, W.J.L. Buyers and H. Hirakawa (1988) Spin dynamics
and the Haldane gap in the spin-1 quasi-one-dimensional antiferromagnet
CsNiCl3. Phys. Rev., B38, 543
Moses, D., E. Ehrenfreund, J. Makovsky and H. Shechter (1977) Magnetic specific
heat of the nearly one-dimensional antiferromagnet CsNiCl3. J. Phys. C: Solid
State Phys., 10, 433
de Neef, T. (1976) Thermodynamics of magnetic chains with S
B13, 4141
Niemeijer, Th. and J.M.J, van Leeuwen (1976) Renormalization theory for Isinglike
spin systems. In C. Domb and M.S. Green (Eds.) Phase Transitions and
Critical Phenomena, Vol. 6, Acad. Press, London, New York and San Francisco,
p. 425
Nickel, B.G. and J.J. Rehr (1990) High-Temperature Series for Scalar Field Lattice
Models: Generations and Analysis J. Stat. Phys., 61, 1
Pawlicki, P., G. Kamieniarz and J.Rogiers (1995) Phase diagram of the extended
Ashkin-Teller model. J. Magn. Magn. Mat., 140-144, 1471
Pearce, P.A. and K.A. Seaton (1990) The off-critical integrable Ashkin-Teller
model. J. Phys. A: Math. Gen., 23, 1191
Privman, V. and M.E. Fisher (1984) Universal critical amplitudes in finite-size
scaling. Phys. Rev., B30, 322
Racz, Z. (1980) Phase boundary of Ising antiferromagnets near H = Hc and
T = 0: Results from hard-core lattice gas calculations. Phys. Rev., B21, 4012
Ramirez, A.P. and W.P. Wolf (1985) Specific heat of CsNiF3. Phys. Rev., B32,
1639
Ramirez, A.P., S.-W. Cheong and M.L. Kaplan (1994) Specific heat of defects in
Haldane systems Y2BaNiO5 and NENP: absence of the spin-1/2 excitations.
Phys.Rev. Lett, 72, 3108
Rosengren, A. (1986) On the combinatorial solution of the Ising model. J. Phys.
A: Math. Gen., 19, 1709
Steiner, M., J. Villain and C.G. Windsor (1976) Theoretical and experimental
studies on one-dimensional magnetic systems. Adv. Phys., 25, 1
Steiner, M. and J.K. Kjems (1977) Spin waves in CsNiF3 with an applied magnetic
field. J. Phys. C: Solid State Phys., 10, 2665
Steiner, M., K. Kakurai and J.K. Kjems (1983) Experimental Study of the Spindynamics
in the 1-D Ferromagnet with Planar Anisotropy: CsNiF3 in an External
Magnetic Field. Z. Phys., B53, 117
5/2. Phys. Rev,
Suzuki M. (1993) Quantum Monte Carlo methods – recent developments. Physica,
A194, 432
Swendsen, R.H. and J.-S. Wang (1988) Nonuniversal Critical Dynamics in Monte
Carlo Simulations. Phys. Rev. Lett., 58, 86
Weng, C.J. (1968) Ph. D. Thesis, Cornegie Institute of Technology
Wolff, U. (1989) Collective Monte Carlo Updating for Spin System. Phys. Rev.
Lett, 62, 361
Wood, D.W. and M. Goldfinch (1980) Vertex models for the hard-square and hard
hexagon gases, and critical parameters from the scaling transformations. J. Phys.
A: Math. Gen., 13, 2781
Recent developments in computer simulations of phase transitions in Ising-like systems and thermodynamic behaviour of quantum spin chains are reviewed. A combination of stochastic Monte Carlo as well as deterministic transfer matrix and finite-size diagonalization methods is described in both fields as regards static properties. Asymptotic analysis and extrapolation techniques are presented in detail. Some effective-field methods, series expansions, spin dynamics simulations and experimental applications are also discussed.
Achiwa, N. (1969) Linear antiferromagnetic chains in hexagonal ABCl3-type compounds (A; Cs or Rb, B;Cu, Ni, Co or Fe). J. Phys. Soc. Jpn., 27, 561
Aharony, A. and M.E. Fisher (1983) Nonlinear scaling fields and corrections to scaling near criticality. Phys. Rev., B27, 4394
Allroth, E. and H.J. Mikeska (1981) Solitons and magnons in sine-Gordon like magnets. Z. Phys., B43, 209
Baillie, C.F., R. Gupta, K.A. Hawick and G.S. Pawley (1992) Monte Carlo renormalization
group studies of the three-dimensional Ising model. Phys. Rev., B45, 10438
Barber, M.N. (1983) Finite-Size Scaling. In C. Domb and J.L. Lebowitz (Eds.),
Phase Transitions and Critical Phenomena, Vol.8, Academic Press, London
Baxter, R.J. (1982) Exactly Solvable Models in Statistical Mechanics. Academic
Press, New York
Baxter^ R.J., I.G. Enting and S.K. Tsang (1980) Hard-square lattice gas. J. Stat.
Phys., 22, 465
Binder, K. (1981) Finite size scaling analysis of Ising model block distribution
functions. Z. Phys., B43, 119
Blöte, H. (1975) The specific heat of magnetic linear chains. Physica, B79, 427
Blöte, H., A. Compa.gner and A. Hoogland (1987) The simple quadratic Ising
model with crossing bonds. Physica, A141, 375
Blöte, H. and G. Kamieniarz (1993) Finite-size calculations of the three-dimensional
Ising model. Physica, A196, 455
Blöte, H. and G. Kamieniarz (1994) Simulations of the 3D Ising model at criticality.
Acta Phys. Polon., A85, 389
Blöte, H. and X.N. Wu (1990) Accurate determination of the critical line of the
square Ising antiferromagnet in afield. J. Phys. A: Math. Gen., 23, L627
Bonner, J.C. and M.E. Fisher (1964) Linear magnetic chains with anisotropic
coupling. Phys. Rev., A135, 640
Bruce, A.D. (1985) Universality in the two-dimensional continuous spin model. J.
Phys. A: Math. Gen., 18, L873
Burkhardt, T.W. and B. Derrida (1985) Moments of the total magnetization and
conformal invariance in the finite two-dimensional Ising model. Phys. Rev., B32,
7273
Cachine, J., J.R. Drugovich de Feli and N. Caticha (1989) Non-universal exponents
and marginal operators via a Monte Carlo renormalisation-group. J. Phys. A:
Math. Gen.,22, 1639
R. Dekeyser, Phys. Rev. B42, 10765 (1990)
Campana, L.S., A. Caramico D’Auria, U. Esposito, G. Kamieniarz and R. Dekeyser
(1990) Specific heat of (C6HnNh3)CuBr3 and (C3HiiNH3)CuC13 within
series analysis of finite chain data. Phys. Rev., B42, 10765
Campana, L.S., A. Caramico D’Auria, F. Esposito, U. Esposito, R.W. Gerling,
and G. Kamieniarz (1992a) Static prperties of quantum spin S=1 chains: TMNB,
TMNC and CsNiF3. J. Phys.: Cond. Matter, 4, 2915
Campana L.S., A. Caramico D’Auria, F. Esposito, U. Esposito, G. Kamieniarz
(1992b) Finite-Chain approach to the study of CsNiCh- Phys. Rev., B45, 5035
Campana, L.S., A. Caramico D’Auria, F. Esposito, U. Esposito and G. Kamieniarz
(1996), Phys. Rev. B
Cardy, J.L. (1987) Conformal Invariance. In C. Domb and J.L. Lebowitz (Eds.)
Phase Transitions and Critical Phenomena Vol. 11 Academic Press, New York
Cuccoli, A., V. Tognetti, P. Verrucchi and R. Vaia (1992) Quantum thermodynamics
of the easy-plane ferromagnetic chain. Phys. Rev., B46, 11601
Cullen, J.J. and D.P. Landau (1983) Monte Carlo studies of one-dimensional quantum
Heisenberg and XY-models. Phys. Rev., B27, 297
Darriet, J. and L.P. Regnault (1993) The compound Y2BaNi05: a new example
of a Haldane-gap in S=1 magnetic chain. Solid State Commun., 86, 409
Dekeyser, R. and G. Kamieniarz (1992) Effective field methods with correlations
in magnetic systems. J. Magn. Magn. Mat., 104-107, 273
Delica, T. and H. Leschke (1990) Formulation and numerical results of the transfer-
matrix method for quantum spin chains. Physica, A168, 736
Delica, T., W.J.M. de Jonge, K. Kopinga, H. Leschke and H.J. Mikeska (1991)
Static properties of CsNiF3: Comparison of numerical results, experimental data
and predictions from soliton-bearing models. Phys. Rev., B44, 11773
Dupas, C. and J.P. Renard (1977) Low-temperature magnetic properties of three
linear S=1 ferromagnets with an easy plane anisotropy: TMNB, TMNC and
CsNiF3. J. Phys. C: Solid State Phys., 10, 5057
Ferrenberg, A.M. and D.P. Landau (1991) Critical behavior of the three-dimensional
Ising model: a high resolution Monte Carlo study. Phys. Rev., B44, 5081
Fisher, M.E. and H. Au-Yang (1979) Inhomogeneous differential approximants for
power series. J. Phys. A: Math. Gen., 12, 1677
Gadet, V., M. Verdaguer, V. Briois, A. Gleizes, J.P. Renard, P. Beauvillain, C.
Chappert, T. Goto, K. Le Dang and P. Veillet (1991) Structural and magnetic
properties of (CH3)4NNi(N02)3: a Haldane-gap system. Phys. Rev., B44, 705
Gatteschi, D., A. Caneschi, L, Pardi and R. Sessoli (1994) Large clusters of metal
ions: the transition from molecular to bulk magnets. Science, 265, 1054
Gerling, R.W. and D.P. Landau (1990) Spin dynamics study of the classical ferromagnetic
XY chain. Phys. Rev., B41, 7139
Grille, H., G. Kamieniarz and R.W. Gerling (1992) Spin dynamics of the classical
easy-plane Heisenberg chain. J. Magn. Magn. Mat., 104-107, 1067
Halperin, B.I. (1992) Quantum antiferromagnets in one and two dimensions. J.
Magn. Magn. Mat., 104-107, 761
Indekeu, J.O., A.Maritan and A.L.Stella (1982) Renormalization group recursions
by mean-field approximations. J. Phys. A: Math. Gen. 15, L291
de Jongh, L.J. and A.R. Miedema (1974) Experiments on simple magnetic model
systems. Adv. Phys., 23, 1
Kakurai, K., M. Steiner and B. Dorner (1990) Study of the spin weave linewidth in
ID easy-plane ferromagnet using neutron polarization analysis. Europhys. Lett.,
12,653
Kamieniarz, G., F. Mallezie and R. Dekeyser (1988) Magnetization and correlation
length of the easy-plane ferromagnetic chain: numerical analysis and application
to (C6HilNH3)CuBr3. Phys. Rev., B38, 6941
Kamieniarz, G. and H.W.J. Blöte (1993a) Universal ratio of magnetization moments
in two-dimensional Ising model. J. Phys. A: Math. Gen., 26, 201
Kamieniarz, G. and H. Blöte (1993b) The non-interacting hard-square lattice gas:
Ising universality. J. Phys. A: Math. Gen., 26, 6679
Kamieniarz, G., G. Musial and R. Dekeyser (1994) Effective field methods for
magnetic systems. Acta Phys. Polon., A85, 413
Kamieniarz, G. and R. Matysiak (1996a), in preparation
Kamieniarz, G., G. Musial and R. Dekeyser (1996b), in preparation
Klümper, A. and P.A. Pearce (1993) New results for exactly solvable critical RSOS
models and vertex models in two dimensions. Physica, A194, 397
Kopinga, K., J. Emmen, G.C. de Vries, L.F. Lemmens and G. Kamieniarz (1988)
Comparison between experiment and numerical calculations on S = l / 2 Heisenberg-
XY ferromagnetics chains. J. de Physique, C8, 1451
Kopinga, K., T. Delica and H. Leschke (1989) Static properties of an easy-plane
ferromagnetics S = l / 2 chain: comparison of numerical results and experimental
data on (C6HiiNH3)CuBr3. Phys. Rev., B40, 7239
Kopinga, K., T. Delica, H. Leschke and I. Riedel (1993) Static properties of a
ferromagnetic S = l / 2 chain system with orthorombic exchange anisotropy: comparison
of numerical results and experimental data on (CgITu NH3)CuCl3. Phys.
Rev., B47, 5447
Landau, D.P. (1994) Computer simulation studies of critical phenomena. Physica,
A205, 41
Le Guillou, J.C. and J. Zinn-Justin (1980) Critical exponents from field theory.
Phys. Rev., B21, 3976
Liu, A.J. and M.E. Fisher (1989) The three-dimensional Ising model revisited
numerically. Physica, A156, 35
Livet, F. (1991) The cluster updating Monte Carlo algorithm applied to the 3D
Ising problem. Europhys. Lett., 16, 139
Heisenberg antiferromagnet on a square lattice
and its applications to the cuprous oxides. Rev. Mod. Phys., 63, 1
Mikeska, H.J. (1978) Solitons in a one-dimensional magnet with an easy plane. J.
Phys. G: Solid State Phys., 11, L29
Manousakis, E. (1991) The spinMikeska,
H.J. and M. Steiner (1991) Solitary excitations in one-dimensional magnets.
Adv. Phys., 40, 191
Morra, R.M., R.M. Armstrong, W.J.L. Buyers and H. Hirakawa (1988) Spin dynamics
and the Haldane gap in the spin-1 quasi-one-dimensional antiferromagnet
CsNiCl3. Phys. Rev., B38, 543
Moses, D., E. Ehrenfreund, J. Makovsky and H. Shechter (1977) Magnetic specific
heat of the nearly one-dimensional antiferromagnet CsNiCl3. J. Phys. C: Solid
State Phys., 10, 433
de Neef, T. (1976) Thermodynamics of magnetic chains with S
B13, 4141
Niemeijer, Th. and J.M.J, van Leeuwen (1976) Renormalization theory for Isinglike
spin systems. In C. Domb and M.S. Green (Eds.) Phase Transitions and
Critical Phenomena, Vol. 6, Acad. Press, London, New York and San Francisco,
p. 425
Nickel, B.G. and J.J. Rehr (1990) High-Temperature Series for Scalar Field Lattice
Models: Generations and Analysis J. Stat. Phys., 61, 1
Pawlicki, P., G. Kamieniarz and J.Rogiers (1995) Phase diagram of the extended
Ashkin-Teller model. J. Magn. Magn. Mat., 140-144, 1471
Pearce, P.A. and K.A. Seaton (1990) The off-critical integrable Ashkin-Teller
model. J. Phys. A: Math. Gen., 23, 1191
Privman, V. and M.E. Fisher (1984) Universal critical amplitudes in finite-size
scaling. Phys. Rev., B30, 322
Racz, Z. (1980) Phase boundary of Ising antiferromagnets near H = Hc and
T = 0: Results from hard-core lattice gas calculations. Phys. Rev., B21, 4012
Ramirez, A.P. and W.P. Wolf (1985) Specific heat of CsNiF3. Phys. Rev., B32,
1639
Ramirez, A.P., S.-W. Cheong and M.L. Kaplan (1994) Specific heat of defects in
Haldane systems Y2BaNiO5 and NENP: absence of the spin-1/2 excitations.
Phys.Rev. Lett, 72, 3108
Rosengren, A. (1986) On the combinatorial solution of the Ising model. J. Phys.
A: Math. Gen., 19, 1709
Steiner, M., J. Villain and C.G. Windsor (1976) Theoretical and experimental
studies on one-dimensional magnetic systems. Adv. Phys., 25, 1
Steiner, M. and J.K. Kjems (1977) Spin waves in CsNiF3 with an applied magnetic
field. J. Phys. C: Solid State Phys., 10, 2665
Steiner, M., K. Kakurai and J.K. Kjems (1983) Experimental Study of the Spindynamics
in the 1-D Ferromagnet with Planar Anisotropy: CsNiF3 in an External
Magnetic Field. Z. Phys., B53, 117
5/2. Phys. Rev,
Suzuki M. (1993) Quantum Monte Carlo methods – recent developments. Physica,
A194, 432
Swendsen, R.H. and J.-S. Wang (1988) Nonuniversal Critical Dynamics in Monte
Carlo Simulations. Phys. Rev. Lett., 58, 86
Weng, C.J. (1968) Ph. D. Thesis, Cornegie Institute of Technology
Wolff, U. (1989) Collective Monte Carlo Updating for Spin System. Phys. Rev.
Lett, 62, 361
Wood, D.W. and M. Goldfinch (1980) Vertex models for the hard-square and hard
hexagon gases, and critical parameters from the scaling transformations. J. Phys.
A: Math. Gen., 13, 2781
