2-Dimensional Ising Models  

In General > s.a. ising models; spin models; lattice field theory [random].
* Motivation: The 2D Ising model is the only non-trivial exactly solvable model of phase transition; 2016, Proof that all classical spin models are equivalent to 2D Ising models, with possibly position-dependent couplings and external fields.
* Summary: Without a magnetic field, one gets the Onsager solution (1940s) with a phase transition, while with a magnetic field exact results were obtained in the 1980s by Zamolodchikov, at the critical temperature.
@ As universal models: De las Cuevas & Cubitt sci(16)mar + summary sci(16)mar.
@ General references: Kac & Ward PR(52) [combinatorial]; Maddox Nat(92)oct [Onsager solution]; de Oliveira et al JPA(06) [Monte Carlo evolution]; García-Pelayo JMP(09) [isomorphism with persistent random walk]; Bostan et al a0904; Strack & Jakubczyk PRB(09)-a0906; Huber & Law a0907 [canonical paths]; Parisen Toldin et al JSP(09) [low-T paramagnetic-ferromagnetic transition]; Mangazeev et al PRE(10)-a1005 [scaling and universality, with magnetic field]; McCoy & Maillard PTP(12)-a1203 [rev]; Camia MPRF-a1205 [continuum scaling limit]; Kager et al JSP(13)-a1208 [signed-loop approach]; Siudem et al a1410 [infinite square lattice partition function, low-temperature expansion]; Chelkak et al a1507 [combinatorics].
@ Susceptibility: Boukraa et al JPA(08)-a0808 [many terms in a series]; McCoy et al a1003 [rev]; Chan et al JSP(11)-a1012 [zero-field, many terms]; Tracy & Widom JMP(13) [diagonal susceptibility].
@ Correlation functions: Bell PR(66); Wang PhyA(09); Perk & Au-Yang JSP(09) [pair-correlation functions]; Iorgov & Lisovyy JSP(11)-a1012; Chelkak et al a1202 [n-point spin correlations].
@ Critical behavior: Lubetzky & Sly CMP(12) [mixing time]; Beffara & Duminil-Copin AP(12)-a1010; Li CMP(12) [periodic models]; Witczak-Krempa PRL(15)-a1501; Assis et al a1705 [analyticity properties].
@ Other specific quantities: Beale PRL(96) [exact energy distribution function]; Schülke & Zheng PLA(97) [global persistence exponent]; Kitatani et al JPA(03) [specific heat, ± J]; Mangazeev et al JPA(09) [scaling function, in magnetic field]; Camia et al a1205 [magnetization exponent]; Baxter JPA(16)-a1606 [square lattice, boundary free energies].
@ Numerical techniques: Nakamura PRL(08) [Monte Carlo, quasi-1D]; Preis et al JCP(09) [GPU-accelerated Monte Carlo].
@ Random field: Moss De Oliveira et al PhyA(90) [and 1D]; > s.a. renormalization.
> Related topics: see entanglement entropy.

Different Types
@ Random lattice: Boulatov & Kazakpv PLB(87) [critical exponents]; Janke et al NPPS(94); Lima et al PhyA(00); De Sanctis a0811; Dommers et al JSP(10)-a1005 [with power-law degree distribution]; Giardinà et al a1412 [central-limit theorems]; Sasakura & Sato PTEP(14)-a1401.
@ Other lattices: Repetowicz et al JPA(99), Repetowicz JPA(02) [quasiperiodic, Penrose tiling]; Oitmaa & Keppert JPA(02) [on a 4-6 lattice]; Bugrij & Lisovyy PLA(03)-a0708 [finite lattice, spin matrix elements], TMP(04)-a0708 [anisotropic lattice, correlation functions]; Wan ht/05 [with non-local links]; Benedetti & Loll GRG(07)gq/06 [on dynamical triangulation]; Balint et al a0806 [triangular lattice]; Björnberg JSP(09) [on star-like graphs]; Viana et al PLA(09) [anisotropic lattice, antiferromagnetic, longitudinal field]; Codello JPA(10) [Archimedean and Laves lattices]; Mellor et al a1106 [Union Jack lattice]; Gandolfo et al JSP(12)-a1207 [Cayley tree, Gibbs states]; Yoshida & Kubica a1404 [on a fractal (Sierpiński) lattice].
@ On causal triangulations: Napolitano & Turova JSP(16)-a1504 [random planar triangulations].
@ Different global topologies: Burda & Jurkiewicz PLB(88) [on T2]; Nigro PhyA(13)-a1010 [cylinder, spatially periodic boundary conditions]; Assis & McCoy JPA(11)-a1011 [half-plane lattice]; Lu & Wu PRE(01)cm/00 [non-orientable surface]; Greenblatt a1409 [cylinder, finite-size corrections]; Matsuura & Sakai a1507 [with twisted boundary conditions]; Mohammed & Mahapatra a1601 [different boundary conditions].
@ Different interactions: Van den Nest et al PRL(08)-a0708 [arbitrary graph with inhomogeneous pairwise interactions equivalent to 2D square lattice with suitable couplings]; Picco a1207, Blanchard et al EPL(13)-a1211 [long-range interactions, simulations of critical behavior].
@ Other variations: Kutlu PhyA(97) [with more interactions]; Roder et al PhyA(99) [high-T analysis]; Bittner et al PhyA(00) [fluctuating]; Dorogovtsev et al PRE(02)cm [Tc]; Shiwa & Sakaniwa JPA(06)cm/05 [on a constant negative curvature surface]; Rojas & de Souza PLA(09) [exactly-solvable models]; Gandolfo et al CMP(15)-a1310 [on the Lobachevsky plane]; Aasen et al JPA(16)-a1601 [with topological defects]; > s.a. ising models.
@ Relationship with different models: Wetterich a1612 [and free massless Dirac fermions in 2D Minkowski space]
> Gravity-related models: see 2D gravity; spin networks.


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