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References

  • Aizenman, M.; Barsky, D. J.; Fernández, R. The phase transition in a general class of Ising-type models is sharp. J. Statist. Phys. 47 (1987), no. 3-4, 343--374. MR0894398
  • Baxter, R. J. Solvable eight-vertex model on an arbitrary planar lattice. Philos. Trans. Roy. Soc. London Ser. A 289 (1978), no. 1359, 315--346. MR0479213
  • Beffara, Vincent; Duminil-Copin, Hugo. The self-dual point of the two-dimensional random-cluster model is critical for $q\geq 1$. Probab. Theory Related Fields 153 (2012), no. 3-4, 511--542. MR2948685
  • V. Beffara and H. Duminil-Copin. Smirnov's fermionic observable away from criticality. Ann. Probab., 40:2667--2689, 2012.
  • Boutillier, Cédric; de Tilière, Béatrice. The critical ${\bf Z}$-invariant Ising model via dimers: the periodic case. Probab. Theory Related Fields 147 (2010), no. 3-4, 379--413. MR2639710
  • Boutillier, Cédric; de Tilière, Béatrice. The critical $Z$-invariant Ising model via dimers: locality property. Comm. Math. Phys. 301 (2011), no. 2, 473--516. MR2764995
  • D. Chelkak and S. Smirnov. Universality in the 2D Ising model and conformal invariance of fermionic observables. to appear in Inv. Math., pages DOI:10.1007/s00222--011--0371--2, 2009.
  • D. Cimasoni. A generalized Kac-Ward formula. J. Stat. Mech., page P07023, 2010.
  • Cimasoni, David. The critical Ising model via Kac-Ward matrices. Comm. Math. Phys. 316 (2012), no. 1, 99--126. MR2989454
  • de Tilière, Béatrice. Quadri-tilings of the plane. Probab. Theory Related Fields 137 (2007), no. 3-4, 487--518. MR2278466
  • Dubédat, Julien. Topics on abelian spin models and related problems. Probab. Surv. 8 (2011), 374--402. MR2861134
  • H. Duminil-Copin and S. Smirnov. Conformal invariance in lattice models. In D. Ellwood, C. Newman, V. Sidoravicius, and W. Werner, editors, Lecture notes, in Probability and Statistical Physics in Two and More Dimensions. CMI/AMS -- Clay Mathematics Institute Proceedings, 2011.
  • Edwards, Robert G.; Sokal, Alan D. Generalization of the Fortuin-Kasteleyn-Swendsen-Wang representation and Monte Carlo algorithm. Phys. Rev. D (3) 38 (1988), no. 6, 2009--2012. MR0965465
  • R.B. Griffiths. Correlation in Ising ferromagnets I, II. J. Math. Phys., 8:478--489, 1967.
  • Grimmett, Geoffrey. The random-cluster model. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 333. Springer-Verlag, Berlin, 2006. xiv+377 pp. ISBN: 978-3-540-32890-2; 3-540-32890-4 MR2243761
  • P. W. Kasteleyn. The statistics of dimers on a lattice. Physica, 27:1209--1225, 1961.
  • Kasteleyn, P. W. Dimer statistics and phase transitions. J. Mathematical Phys. 4 1963 287--293. MR0153427
  • Kasteleyn, P. W. Graph theory and crystal physics. 1967 Graph Theory and Theoretical Physics pp. 43--110 Academic Press, London MR0253689
  • D.G. Kelly and S. Sherman. General Griffiths's inequality on correlation in Ising ferromagnets. J. Math. Phys., 9:466--484, 1968.
  • Kenyon, Richard; Okounkov, Andrei. Planar dimers and Harnack curves. Duke Math. J. 131 (2006), no. 3, 499--524. MR2219249
  • Kenyon, Richard; Okounkov, Andrei; Sheffield, Scott. Dimers and amoebae. Ann. of Math. (2) 163 (2006), no. 3, 1019--1056. MR2215138
  • Kramers, H. A.; Wannier, G. H. Statistics of the two-dimensional ferromagnet. I. Phys. Rev. (2) 60, (1941). 252--262. MR0004803
  • Lebowitz, J. L.; Pfister, C. E. Surface tension and phase coexistence. Phys. Rev. Lett. 46 (1981), no. 15, 1031--1033. MR0607430
  • Lebowitz, Joel L. GHS and other inequalities. Comm. Math. Phys. 35 (1974), 87--92. MR0339738
  • W. Lenz. Beitrag zum verständnis der magnetischen eigenschaften in festen körpern. Phys. Zeitschr., 21:613--615, 1920.
  • Li, Zhongyang. Critical temperature of periodic Ising models. Comm. Math. Phys. 315 (2012), no. 2, 337--381. MR2971729
  • Zhongyang Li. Spectral Curve of Periodic Fisher Graphs. arXiv:1008.3936v5 [math.CV], April 2012.
  • B.M. McCoy and T.T. Wu. The two-dimensional Ising model. Harvard University Press, Cambridge, MA, 1973.
  • Mikhalkin, Grigory; Rullgård, Hans. Amoebas of maximal area. Internat. Math. Res. Notices 2001, no. 9, 441--451. MR1829380
  • Onsager, Lars. Crystal statistics. I. A two-dimensional model with an order-disorder transition. Phys. Rev. (2) 65, (1944). 117--149. MR0010315
  • R. Peierls. On ising's model of ferromagnetism. Math. Proc. Camb. Phil. Soc., 32:477--481, 1936.
  • Serre, Jean-Pierre. Arbres, amalgames, ${\rm SL}_{2}$. (French) Avec un sommaire anglais. Rédigé avec la collaboration de Hyman Bass. Astérisque, No. 46. Société Mathématique de France, Paris, 1977. 189 pp. (1 plate). MR0476875
  • Sheffield, Scott. Random surfaces. Astérisque No. 304 (2005), vi+175 pp. MR2251117
  • Simon, Barry. Correlation inequalities and the decay of correlations in ferromagnets. Comm. Math. Phys. 77 (1980), no. 2, 111--126. MR0589426
  • B. L. van~der Waerden. Die lange Reichweite der regelmassigen Atomanordnung in Mischkristallen. Z. Physik, 118:473--488, 1941.
  • F. Y. Wu and K. Y. Lin. Staggered ice-rule vertex modelhar22the pfaffian solution. Phys. Rev. B, 12:419--428, Jul 1975.


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