upward

Ising model

Blote H W J, Heringa J R, Simulations of Ising models (2002)

Equilibrium properties

Short-range interaction

Haggkvist R, Rosengren A, Lundow P H, Markstrom K, Andren D, Kundrotas P, On the Ising model for the simple cubic lattice, AP 56, 653 (2007)


A Ferrenberg, J Xu, D Landau, Pushing the limits of Monte Carlo simulations for the three-dimensional Ising model, PRE 97, 043301 (2018) – doi

Юрищев М А, Критические свойства высокоспиновых моделей изинга на анизотропной решетке, ЖЭТФ 130, 931 (2006)

Kaupuzs J, Surface tension and interfacial fluctuations in d-dimensional Ising model, Int J Mod Phys C 12, 1121 (2005)

Qian X, Blote H W J, Triangular Ising model with nearest- and next-nearest-neighbor couplings in a field, PRE 70, 036112 (2004)

Butera P, Comi M, Updated tests of scaling and universality for the spin-spin correlations in the 2D and 3D spin-S Ising models using high-temperature expansions, hep-lat/0406035

Butera P, Comi M, Guttmann A J, Critical parameters and universal amplitude ratios of two-dimensional spin-S Ising models using high- and low-temperature expansions, PRE 67, 054402 (2003)

Campanino M, Ioffe D, Velenik Y, Rigorous nonpertubative Ornstein-Zernike theory for Ising ferromagnets, Europhys Lett 62, 182 (2003)

Garcia J G, Gonzalo J A, Monte Carlo critical isotherms for Ising lattices, cond-mat/0304056

Arisue H, Fujiwara T, New algorithm of the finite lattice method for the high-temperature expansion of the Ising model in three dimensions, PRE 67, 066109 (2003)

Rubtsov A N, Is the mean-field approximation so bad? A simple generalization yieldind realistic critical indices for 3D Ising-class systems, cond-mat/0201147

Kaupuzs J, Transfer matrix and Monte Carlo tests of critical exponents in lattice models, cond-mat/0201221

Ivashkevich E V, Izmailian N S, Hu C, Kronecker’s double series and exact asymptotic expansions for free models of statistical mechanics on torus, JPA 35, 5543 (2002)

Campostrini M, Pelissetto A, Rossi P, Vicari E, 25th-order high-temperature expansion results for three-dimensional Ising-like systems on the simple cubic lattice, cond-mat/0201180

Blote H W J, Heringa J R, Tsypin M M, Three-dimensional Ising model in the fixed-magnetization ensemble: A Monte Carlo study, PRE 62, 77 (2000)

Lou S L, Wu S H, Three-dimensional Ising model and transfer matrices, cond-mat/0003367

Bhanot G, Creutz M, Horvath I, Lacki J, Weckel J, Series expansion without diagrams, PRE 49, 2445 (1994)

D Pini, A Parola, L Reatto, Hierarchical reference theory of fluids: Application to three-dimensional Ising model, JSP 72, 1179 (1993) – doi

Bhanot G, Creutz M, Lacki J, Low temperature expansion for the Ising model, PRL 69, 1841 (1992)

Creutz M, State counting and low-temperature series, PRB 43, 10659 (1991)

Georges A, Yedidia J S, How to expand around mean-field theory using high-temperature expansions, JPA 24, 2173 (1991)

He H X, Hamer C J, Oitmaa J, High-temperature series expansions for the (2+1)-dimensional Ising model, JPA 23, 1775 (1990)

Adler J, Critical temperatures of the d=3, s=1/2 Ising model; the effect of confluent corrections to scaling, JPA 16, 3585 (1983)

Sykes M F, Hunter D L, Low-temperature expansion data for the Ising model: simple cubic and simple quadratic lattices, JPA 13, 1121 (1980)

Sykes M F, Derivation of low-temperature expansions for Ising model X. The four-dimensional simple hypercubic lattice, JPA 12, 879 (1979)

Sykes M F, McKenzie S, Watts M G, Gaunt D S, Derivation of low-temperature expansions for Ising model IX. High-field polynomials for the honeycomb-triangular system, JPA 8, 1461 (1975)

Sykes M F, Watts M G, Gaunt D S, Derivation of low-temperature expansions for Ising model VIII. Ferromagnetic and antiferromagnetic polynomials for the honeycomb-triangular system, JPA 8, 1448 (1975) – cor

Sykes M F, Watts M G, Gaunt D S, Derivation of low-temperature expansions for Ising model VII. The honeycomb-triangular code system, JPA 8, 1441 (1975)

Sykes M F, Watts M G, Derivation of low-temperature expansions for the Ising model with triplet interactions on the plane triangular lattice, JPA 8, 1469 (1975)

Sykes M F, Gaunt D S, Essam J W, Elliott C J, Derivation of low-temperature expansions for Ising model VI. Three-dimensional lattices - temperature grouping, JPA 6, 1507 (1973)

Sykes M F, Gaunt D S, Essam J W, Heap B R, Elliott C J, Mattingly S R, Derivation of low-temperature expansions for Ising model V. Three-dimensional lattices - field grouping, JPA 6, 1498 (1973)

Sykes M F, Gaunt D S, Martin J L, Mattingly S R, Essam J W, Derivation of low-temperature expansions for Ising model. IV. Two-dimensional lattices-temperature grouping, JMP 14, 1071 (1973)

Sykes M F, Gaunt D S, Mattingly S R, Essam J W, Elliott C J, Derivation of low-temperature expansions for Ising model. III. Two-dimensional lattices-field grouping, JMP 14, 1066 (1973)

Sykes M F, Gaunt D S, Essam J W, Hunter D L, Derivation of low-temperature expansions for Ising model. II. General theory, JMP 14, 1060 (1973)

Sykes M F, Essam J W, Gaunt D S, Derivation of low-temperature expansions for the Ising model of a ferromagnet and an antiferromagnet. I, JMP 6, 283 (1965)

Sykes M F, Gaunt D S, Roberts P D, Wyles J A, High temperature series for the susceptibility of the Ising model II. Three dimensional lattices, JPA 5, 640 (1972)

Sykes M F, Gaunt D S, Roberts P D, Wyles J A, High temperature series for the susceptibility of the Ising model I. Two dimensional lattices, JPA 5, 624 (1972)

Sykes M F, Fisher M E, Susceptibility of the Ising model of an antiferromagnet, PRL 1, 321 (1958)

Long-range interaction

Cannas S A, Gleiser P M, Tamarit F A, Two dimensional Ising model with long-range competing interactions, cond-mat/0502403

2D Ising model

Delfino G, Integrable field theory and critical phenomena: the Ising model in a magnetic field, JPA 37, R45 (2004)

McCoy B M, Wu T T, The two-dimensional Ising model (Harvard Univ. Press, Cambridge, Mass., 1973)


N Iorgov, O Lisovyy, Ising Correlations and Elliptic Determinants, JSP 143, 33 (2011)

Boukraa S, Guttmann A J, Hassani S, Jensen I, Maillard J-M, Nickel B, Zenine N, Experimental mathematics on the magnetic susceptibility of the square lattice Ising model, JPA 41, 455202 (2008)

Janke W, Schakel A M, Fractal structure of spin clusters and domain walls in the two-dimensional Ising model, PRE 71, 036703 (2005)

Hilfer R, Biswal B, Mattutis H G, Janke W, Multicanonical simulations of the tails of the order-parameter distribution of the two-dimensional Ising model, cond-mat/0502408

Zenine N, Boukraa S, Hassani S, Maillard J-M, Ising model susceptibility: the Fuchsian differential equation for c(4) and its factorization properties, JPA 38, 4149 (2005)

Zenine N, Boukraa S, Hassani S, Maillard J-M, Square lattice Ising model susceptibility: series expansion method and differential equation for c(3), JPA 38, 1875 (2005)

Kim S Y, Yang-Lee zeros of the antiferromagnetic Ising model, PRL 93, 130604 (2004)

Lu W T, Wu F Y, Soluble kagome Ising model in a magnetic field, cond-mat/0409083

da Costa G A T F, Maciel A L, Combinatorial formulation of Ising model revisited, math-ph/0304033

Kaupuzs J, Transfer matrix and Monte Carlo tests of critical exponents in Ising model, cond-mat/0405197

Au-Yang H, Perk J H H, Correlation functions and susceptibility in the Z-invariant Ising model, in MathPhys Odyssey 2001: Integrable models and beyond, ed Kashiwara M, Miwa T (Birkhauser, Boston, 2002), 23-48 pp

Oitmaa J, Keppert M, Exact solution of the Ising model on a 4-6 lattice, JPA 35, L219 (2002)

Fortunato S, Site percolation and phase transitions in two dimensions, PRB 66, 054107 (2002)

Orrick W P, Nickel B G, Guttmann A J, Perk J H H, Critical behavior of the two-dimensional Ising susceptibility, PRL 86, 4120 (2001)

Bugrij A I, Form factor representation of the correlation function of the two dimensional ising model on a cylinder, hep-th/0107117

Bugrij A I, Lisovy O O, Magnetic susceptibility of the 2D Ising model on the finite lattice, hep-th/0106270

Caselle M, Hasenbusch M, Pelissetto A, Vicari E, The critical equation of state of the two-dimensional Ising model, JPA 34, 2923 (2001)

Repetowicz P, Finite-lattice expansion for the Ising model on the Penrose tiling, JPA 35, 7753 (2002)

Salas J, Exact finite-size-scaling corrections to the critical two-dimensional Ising model on a torus, cond-mat/0009054

Repetowicz P, Grimm U, Schreiber M, High-temperature expansion for Ising models on quasiperiodic tilings, JPA 32, 4397 (1999)

Salas J, Low-temperature series for renormalized operators: the ferromagnetic square-lattice model, preprint NYU-TH-94

McCoy B M, Perk H H, Wu T T, Ising field theory: Quadratic difference equations for the n-point Green's functions on the lattice, PRL 46, 757 (1981)

Perk J H H, Quadratic identities for Ising model correlations, PLA 79, 3 (1980)

Montroll E W, Potts R B, Ward J C, Correlations and spontaneous magnetization of the two-dimensional Ising model, JMP 4, 308 (1963)

Mathematical

M Biskup, L Chayes, R Kotecky, A proof of the Gibbs-Thomson formula in the droplet formation regime, JSP 116, 175 (2004)

M Biskup, L Chayes, R Kotecky, Critical region for droplet formation in the two-dimensional Ising model, Commun Math Phys 242, 137 (2003)

Miscellaneous

E Flores-Sola, B Berche, R Kenna, M Weigel, Role of Fourier Modes in Finite-Size Scaling above the Upper Critical Dimension, PRL 116, 115701 (2016) – doi

V Sessak, R Monasson, Small-correlation expansions for the inverse Ising problem, JPA 42, 055001 (2009)

Kinetics

Krzakala F, Glassy properties of the Kawasaki dynamics of two-dimensional ferromagnets, PRL 94, 077204 (2005)

Brendel K, Barkema G T, van Beijeren H, Nucleation times in the two-dimensional Ising model, PRE 71, 031601 (2005)

Grynberg M D, Stinchcombe R B, Quantum approach to nucleation times of kinetic Ising ferromagnets, cond-mat/0501351

Sundaramurthy P, Stein D L, Zero-temperature dynamics of 2D and 3D Ising ferromagnets, JPA 38, 349 (2005)

Corberi F, Lippiello E, Zannetti M, Correction to scaling in the response function of the 2d kinetic Ising model, cond-mat/0410712

Robb D T, Novotny M A, Rikvold P A, FORC Analysis of homogeneous nucleation in the two-dimensional kinetic Ising model, cond-mat/0409091

Hurtado P I, Garrido P L, Marro J, Analysis of the interface in a nonequilibrium two-temperature Ising model, PRB 70, 245409 (2004)

Pan A C, Chandler D, Dynamics of nucleation in the Ising model, cond-mat/0408331

Mayer P, Berthier L, Garrahan J P, Sollich P, Fluctuation-dissipation relations in the nonequilibrium critical dynamics of Ising models, PRE 68, 016116 (2003)

Zhu J-Y, Yang Z R, Glauber critical dynamics: Exact solution of the kinetic gaussian model, PRE 59, 1551 (1999)

Wang J-S, Gan C K, Nonequilibrium relaxation of the two-dimensional Ising model: Series-expansion and Monte Carlo studies, PRE 57, 6548 (1998)

Takano H, Miyashita S, Ordering process in the kinetic Ising model on the honeycomb lattice, PRB 48, 7221 (1993)

Nakanishi H, Numerical diagonalization of the Glauber dynamics above and below the transition temperature, PRB 46, 10884 (1992)

Takano H, Nakanishi H, Miyashita S, Stretched-exponential decay of the spin-correlation function in the kinetic Ising model below the critical temperature, PRB 37, 3716 (1988)

Amar J G, Sullivan F E, Mountain R D, Monte Carlo study of growth in the two-dimensional spin-exchange kinetic Ising model, PRB 37, 196 (1988)

Heilig S J, Luscombe J, Mazenko G F, Oguz E, Valls O T, Dynamic correlations in the spin-conserving two-dimensional kinetic Ising model, PRB 25, 7003 (1982)

Mazenko G F, Hirsch J E, Nolan M J, Valls O T, Real-space dynamic renormalization group. III. Calculation of correlation function, PRB 23, 1431 (1981)

Huang H W, First-order approximation for the time-dependent Ising model, PRB 11, 1144 (1975)

Stoll E, Binder K, Schneider T, Monte Carlo investigation of dynamic critical phenomena in the two-dimensional kinetic Ising model, PRB 8, 3266 (1973)

Anderson F B, Green's-function analysis of the Ising ferromagnet, PRB 3, 3950 (1971)

Kawasaki K, Diffusion constants near the critical point for time-dependent Ising models. I, PR 145, 224 (1966)

Kawasaki K, Diffusion constants near the critical point for time-dependent Ising models. II, PR 148, 375 (1966)

Kawasaki K, Diffusion constants near the critical point for time-dependent Ising models. III. Self-diffusion constant, PR 150, 285 (1966)

Heims S P, Master equation for Ising model, PR 138, A587 (1965)

Heims S P, Study of oscillations and correlations in the relaxation of a model spin system, PR 136, A168 (1964)

Glauber R J, Time-dependent statistics of the Ising model, JMP 4, 294 (1963)

Mathematical

Bodineau T, Martinelli F, Some new results on the kinetic Ising model in a pure phase, preprint (2002)

Bovier A, Manzo F, Metastability in Glauber dynamics in the low-temperature limit: Beyond exponential asymptotics, cond-mat/0107376

Martinelli F, Lectures on Glauber dynamics for discrete spin models, LNM 1717, 93 (1999)