References

• J. Ashkin and E. Teller. Statistics of two-dimensional lattices with four components. Phys. Rev., 64:178--184, Sep 1943.
• 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. Cimasoni and H. Duminil-Copin. The critical temperature for the Ising model on planar doubly periodic graphs. ArXiv e-prints, September 2012.
• D. Chelkak, C. Hongler, and K. Izyurov. Conformal Invariance of Spin Correlations in the Planar Ising Model. ArXiv e-prints, February 2012.
• Cimasoni, David; Reshetikhin, Nicolai. Dimers on surface graphs and spin structures. I. Comm. Math. Phys. 275 (2007), no. 1, 187--208. MR2335773
• Cimasoni, David; Reshetikhin, Nicolai. Dimers on surface graphs and spin structures. II. Comm. Math. Phys. 281 (2008), no. 2, 445--468. MR2410902
• D. Chelkak and S. Smirnov. Universality in the 2D Ising model and conformal invariance of fermionic observables. Invent. Math., pages 1--66, 2009.
• de Tilière, Béatrice. Quadri-tilings of the plane. Probab. Theory Related Fields 137 (2007), no. 3-4, 487--518. MR2278466
• B. de~Tilière. Scaling limit of isoradial dimer models and the case of triangular quadri-tilings. Ann. Inst. H. Poincaré Probab. Statist., 43(6):729--750, 2007.
• J. Dubédat. Dimers and analytic torsion I. ArXiv e-prints, October 2011.
• J. Dubédat. Exact bosonization of the Ising model. ArXiv e-prints, December 2011.
• Dolbilin, N. P.; Zinovʹev, Yu. M.; Mishchenko, A. S.; Shtanʹko, M. A.; Shtogrin, M. I. Homological properties of two-dimensional coverings of lattices on surfaces. (Russian) Funktsional. Anal. i Prilozhen. 30 (1996), no. 3, 19--33, 95; translation in Funct. Anal. Appl. 30 (1996), no. 3, 163--173 (1997) MR1435135
• C. Fan. On critical properties of the ashkin-teller model. Phys. Lett. A, 39(2):136, 1972.
• M. E. Fisher. On the dimer solution of planar Ising models. J. Math. Phys., 7:1776--1781, October 1966.
• Fulton, William. Algebraic topology. A first course. Graduate Texts in Mathematics, 153. Springer-Verlag, New York, 1995. xviii+430 pp. ISBN: 0-387-94326-9; 0-387-94327-7 MR1343250
• C. Fan and F. Y. Wu. General lattice model of phase transitions. Phys. Rev. B, 2:723--733, Aug 1970.
• Galluccio, Anna; Loebl, Martin. On the theory of Pfaffian orientations. I. Perfect matchings and permanents. Electron. J. Combin. 6 (1999), Research Paper 6, 18 pp. (electronic). MR1670286
• Ikhlef, Yacine; Rajabpour, Mohammad Ali. Discrete holomorphic parafermions in the Ashkin-Teller model and SLE. J. Phys. A 44 (2011), no. 4, 042001, 11 pp. MR2754707
• P. W. Kasteleyn. The statistics of dimers on a lattice: I. the number of dimer arrangements on a quadratic lattice. Physica, 27:1209--1225, December 1961.
• Kasteleyn, P. W. Graph theory and crystal physics. 1967 Graph Theory and Theoretical Physics pp. 43--110 Academic Press, London MR0253689
• L. Kadanoff and A. C. Brown. Correlation functions on the critical lines of the Baxter and Ashkin-Teller models. Ann. Phys., 121(1–2):318--342, 1979.
• Kadanoff, Leo P.; Ceva, Horacio. Determination of an operator algebra for the two-dimensional Ising model. Phys. Rev. B (3) 3 (1971), 3918--3939. MR0389111
• Kenyon, R. The Laplacian and Dirac operators on critical planar graphs. Invent. Math. 150 (2002), no. 2, 409--439. MR1933589
• Kenyon, Richard; Okounkov, Andrei; Sheffield, Scott. Dimers and amoebae. Ann. of Math. (2) 163 (2006), no. 3, 1019--1056. MR2215138
• Kenyon, Richard; Schlenker, Jean-Marc. Rhombic embeddings of planar quad-graphs. Trans. Amer. Math. Soc. 357 (2005), no. 9, 3443--3458 (electronic). MR2146632
• Kramers, H. A.; Wannier, G. H. Statistics of the two-dimensional ferromagnet. I. Phys. Rev. (2) 60, (1941). 252--262. MR0004803
• Kramers, H. A.; Wannier, G. H. Statistics of the two-dimensional ferromagnet. II. Phys. Rev. (2) 60, (1941). 263--276. MR0004804
• M. Kac and J. C. Ward. A combinatorial solution of the two-dimensional Ising model. Phys. Rev., 88:1332--1337, Dec 1952.
• L. P. Kadanoff and F. J. Wegner. Some critical properties of the eight-vertex model. Phys. Rev. B, 4:3989--3993, Dec 1971.
• Li, Zhi Bing; Guo, Shuo Hong. Duality for the Ising model on a random lattice and topologic excitons. Nuclear Phys. B 413 (1994), no. 3, 723--734. MR1262557
• Z. Li. Spectral Curve of Periodic Fisher Graphs. ArXiv e-prints, August 2010.
• Li, Zhongyang. Critical Temperature of Periodic Ising Models. Comm. Math. Phys. 315 (2012), no. 2, 337--381. MR2971729
• E. H. Lieb. Residual entropy of square ice. Phys. Rev., 162:162--172, Oct 1967.
• Massey, William S. A basic course in algebraic topology. Graduate Texts in Mathematics, 127. Springer-Verlag, New York, 1991. xvi+428 pp. ISBN: 0-387-97430-X MR1095046
• Maunder, C. R. F. Algebraic topology. Reprint of the 1980 edition. Dover Publications, Inc., Mineola, NY, 1996. viii+375 pp. ISBN: 0-486-69131-4 MR1402473
• Nienhuis, Bernard. Critical behavior of two-dimensional spin models and charge asymmetry in the Coulomb gas. J. Statist. Phys. 34 (1984), no. 5-6, 731--761. MR0751711
• Percus, Jerome K. One more technique for the dimer problem. J. Mathematical Phys. 10 1969 1881--1888. MR0250899
• M. Picco and R. Santachiara. Critical interfaces and duality in the Ashkin-Teller model. Phys. Rev. E, 83:061124, Jun 2011.
• Saleur, H. Partition functions of the two-dimensional Ashkin-Teller model on the critical line. J. Phys. A 20 (1987), no. 16, L1127--L1133. MR0924717
• Schramm, Oded; Sheffield, Scott. Contour lines of the two-dimensional discrete Gaussian free field. Acta Math. 202 (2009), no. 1, 21--137. MR2486487
• B. Sutherland. Two-dimensional hydrogen bonded crystals without the ice rule. J. Math. Phys., 11(11):3183--3186, 1970.
• Tesler, Glenn. Matchings in graphs on non-orientable surfaces. J. Combin. Theory Ser. B 78 (2000), no. 2, 198--231. MR1750896
• G. H. Wannier. The statistical problem in cooperative phenomena. Rev. Mod. Phys., 17(1):50--60, Jan 1945.
• F. J. Wegner. Duality relation between the Ashkin-Teller and the eight-vertex model. J. of Phys. C: Solid State Physics, 5(11):L131, 1972.
• D. B. Wilson. XOR-Ising loops and the Gaussian free field. ArXiv e-prints, February 2011.
• F. Y. Wu and K. Y. Lin. Staggered ice-rule vertex model -- the Pfaffian solution. Phys. Rev. B, 12:419--428, Jul 1975.
• F. W. Wu. Ising model with four-spin interactions. Phys. Rev. B, 4:2312--2314, Oct 1971.