E. Bolthausen, F. Caravenna, and B. De-tilière, The quenched critical point of a diluted disordered polymer model. Stochastic Process, Appl, vol.119, issue.5, pp.1479-1504, 2009.

C. Boutillier and B. De-tilière, Loop statistics in the toroidal honeycomb dimer model, The Annals of Probability, vol.37, issue.5, pp.1747-1777, 2009.
DOI : 10.1214/09-AOP453
URL : https://hal.archives-ouvertes.fr/hal-00431839

C. Boutillier and B. De-tilière, The critical Z-invariant Ising model via dimers: the periodic case. Probab. Theory Related Fields, pp.379-413, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00494462

C. Boutillier and B. De-tilière, The Critical Z-Invariant Ising Model via Dimers: Locality Property, Communications in Mathematical Physics, vol.65, issue.3-4, pp.473-516, 2011.
DOI : 10.1007/s00220-010-1151-3
URL : https://hal.archives-ouvertes.fr/hal-00361365

C. Boutillier and B. De-tilière, Height representation of XOR-Ising loops via bipartite dimers, Electronic Journal of Probability, vol.19, issue.0, 2012.
DOI : 10.1214/EJP.v19-2449
URL : https://hal.archives-ouvertes.fr/hal-00755394

C. Boutillier and B. Tilière, Statistical Mechanics on Isoradial Graphs, Springer Proceedings in Mathematics, vol.11, pp.491-512, 2012.
DOI : 10.1007/978-3-642-23811-6_20
URL : https://hal.archives-ouvertes.fr/hal-00705781

B. De-tilière, Partition function of periodic isoradial dimer models. Probab. Theory Related Fields, pp.451-462, 2007.

B. De-tilière, Quadri-tilings of the plane. Probab. Theory Related Fields, pp.487-518, 2007.

B. De-tilière, Scaling limit of isoradial dimer models and the case of triangular quadri-tilings, Annales de l'Institut Henri Poincare (B) Probability and Statistics, vol.43, issue.6, pp.729-750, 2007.
DOI : 10.1016/j.anihpb.2006.10.002

B. De-tilière, Principal minors Pfaffian half-tree theorem. Arxiv: 1207, 2012.

B. De-tilière, From Cycle Rooted Spanning Forests to the Critical Ising Model: an Explicit Construction, Communications in Mathematical Physics, vol.6, issue.68, pp.69-110, 2013.
DOI : 10.1007/s00220-013-1668-3

]. A. Abd04 and . Abdesselam, The Grassmann?Berezin calculus and theorems of the matrix-tree type, Bibliography Adv. in Appl. Math, vol.33, issue.1, pp.51-70, 2004.

E. [. Ashkin and . Teller, Statistics of Two-Dimensional Lattices with Four Components, Physical Review, vol.64, issue.5-6, pp.178-184, 1943.
DOI : 10.1103/PhysRev.64.178

]. R. Bax86 and . Baxter, Free-fermion, checkerboard and Z-invariant lattice models in statistical mechanics, Proc. Roy. Soc. London Ser. A, pp.4041-4074, 1826.

]. R. Bax89 and . Baxter, Exactly solved models in statistical mechanics, 1989.

V. Beffara and H. Duminil-copin, Smirnov???s fermionic observable away from criticality, The Annals of Probability, vol.40, issue.6, pp.2667-2689, 2012.
DOI : 10.1214/11-AOP689
URL : http://arxiv.org/abs/1010.0526

]. E. Bdh97, F. Bolthausen, and . Hollander, Localization transition for a polymer near an interface, Ann. Probab, vol.25, issue.3, pp.1334-1366, 1997.

T. Bodineau and G. Giacomin, On the Localization Transition of Random Copolymers Near Selective Interfaces, Journal of Statistical Physics, vol.117, issue.5-6, pp.801-818, 2004.
DOI : 10.1007/s10955-004-5705-7
URL : https://hal.archives-ouvertes.fr/hal-00103543

E. Bolthausen, F. Hollander, and A. A. Opoku, A copolymer near a selective interface: Variational characterization of the free energy, The Annals of Probability, vol.43, issue.2, pp.1110-1315, 2011.
DOI : 10.1214/14-AOP880

C. [. Bobenko, Y. B. Mercat, and . Suris, Linear and nonlinear theories of discrete analytic functions. Integrable structure and isomonodromic Green???s function, Journal f??r die reine und angewandte Mathematik (Crelles Journal), vol.2005, issue.583, pp.117-161, 2005.
DOI : 10.1515/crll.2005.2005.583.117
URL : https://hal.archives-ouvertes.fr/hal-00250195

]. N. Bou70 and . Bourbaki, Éléments de mathématique, Algèbre. Chapitres, vol.1, issue.3, 1970.

R. [. Burton and . Pemantle, Local Characteristics, Entropy and Limit Theorems for Spanning Trees and Domino Tilings Via Transfer-Impedances, The Annals of Probability, vol.21, issue.3, pp.1329-1371, 1993.
DOI : 10.1214/aop/1176989121
URL : http://arxiv.org/abs/math/0404048

H. [. Cimasoni and . Duminil-copin, The critical temperature for the Ising model on planar doubly periodic graphs, Electronic Journal of Probability, vol.18, issue.0, pp.1-18, 2013.
DOI : 10.1214/EJP.v18-2352

F. Caravenna, G. Giacomin, and M. Gubinelli, A Numerical Approach to Copolymers at Selective Interfaces, Journal of Statistical Physics, vol.46, issue.4, pp.799-832, 2006.
DOI : 10.1007/s10955-005-8081-z
URL : https://hal.archives-ouvertes.fr/hal-00086240

]. S. Cha82 and . Chaiken, A combinatorial proof of the all minors matrix tree theorem, SIAM J. Algebraic Discrete Methods, vol.3, issue.3, pp.319-329, 1982.

C. [. Chelkak, K. Hongler, and . Izyurov, Conformal invariance of spin correlations in~the~planar Ising model, Annals of Mathematics, 1202.
DOI : 10.4007/annals.2015.181.3.5

D. Cimasoni, The Critical Ising Model via Kac-Ward Matrices, Communications in Mathematical Physics, vol.17, issue.1, pp.99-126, 2012.
DOI : 10.1007/s00220-012-1575-z

R. [. Cohn, J. Kenyon, and . Propp, A variational principle for domino tilings, Journal of the American Mathematical Society, vol.14, issue.02, pp.297-346, 2001.
DOI : 10.1090/S0894-0347-00-00355-6

D. Cimasoni and N. Reshetikhin, Dimers on Surface Graphs and Spin Structures. I, Communications in Mathematical Physics, vol.78, issue.1, pp.187-208, 2007.
DOI : 10.1007/s00220-007-0302-7

N. [. Cimasoni and . Reshetikhin, Dimers on Surface Graphs and Spin Structures. I, Communications in Mathematical Physics, vol.78, issue.1, pp.445-468, 2008.
DOI : 10.1007/s00220-007-0302-7

S. [. Chelkak and . Smirnov, Discrete complex analysis on isoradial graphs, Advances in Mathematics, vol.228, issue.3, pp.1590-1630, 2011.
DOI : 10.1016/j.aim.2011.06.025

S. [. Chelkak and . Smirnov, Universality in the 2D Ising model and conformal invariance of fermionic observables, Inventiones mathematicae, vol.172, issue.3, pp.515-580, 2012.
DOI : 10.1007/s00222-011-0371-2

]. J. Dub11a and . Dubédat, Dimers and analytic torsion I. ArXiv: 1110, 2011.

J. Dubédat, Exact bosonization of the Ising model, 2011.

]. R. Duf68 and . Duffin, Potential theory on a rhombic lattice, J. Combinatorial Theory, vol.5, pp.258-272, 1968.

. P. Dzm-+-96-]-n, Y. M. Dolbilin, ?. Zinov, A. S. Ev, M. A. Mishchenko et al., Homological properties of two-dimensional coverings of lattices on surfaces, Funktsional. Anal. i Prilozhen, vol.30, issue.3, pp.19-33, 1996.

]. C. Fan72 and . Fan, On critical properties of the Ashkin-Teller model, Physics Letters A, vol.39, issue.2, pp.136-1972
DOI : 10.1016/0375-9601(72)91051-1

]. A. Fer67 and . Ferdinand, Statistical mechanics of dimers on a quadratic lattice, J. Math. Phys, vol.8, p.2332, 1967.

]. M. Fis66 and . Fisher, On the dimer solution of planar Ising models, J. Math, Phys, vol.7, pp.1776-1781, 1966.

C. M. , F. Piet, and W. Kasteleyn, On the random-cluster model: I. Introduction and relation to other models, Physica, vol.57, issue.4, pp.536-564, 1972.

R. H. Formanfr37-]-r, G. S. Fowler, and . Rushbrooke, Determinants of Laplacians on graphs An attempt to extend the statistical theory of perfect solutions, Topology Transactions of the Faraday Society, vol.32, issue.33, pp.35-461272, 1937.

C. Fan and F. Y. Wu, General Lattice Model of Phase Transitions, Physical Review B, vol.2, issue.3, pp.723-733, 1970.
DOI : 10.1103/PhysRevB.2.723

]. G. Gia07, . [. Giacomin, M. Galluccio, and . Loebl, Random polymer models. Imperial College Pr On the theory of Pfaffian orientations. I. Perfect matchings and permanents, Electron. J. Combin, vol.6, issue.1, p.6, 1999.

G. R. Grimmett and I. Manolescu, Inhomogeneous bond percolation on square, triangular and hexagonal lattices, The Annals of Probability, vol.41, issue.4, 2011.
DOI : 10.1214/11-AOP729
URL : http://arxiv.org/abs/1105.5535

G. R. Grimmett and I. Manolescu, Bond percolation on isoradial graphs: criticality and universality, Probability Theory and Related Fields, vol.13, issue.3, 2012.
DOI : 10.1007/s00440-013-0507-y
URL : http://arxiv.org/abs/1204.0505

]. G. Gri06 and . Grimmett, The random-cluster model, 2006.

G. Giacomin and F. L. Toninelli, Estimates on path delocalization for copolymers at interfaces. Probab. Theory Related Fields, pp.464-482, 2005.
URL : https://hal.archives-ouvertes.fr/hal-00014639

S. Hirschman and V. Reiner, Note on the Pfaffian Matrix-Tree Theorem, Graphs and Combinatorics, vol.20, issue.1, pp.59-63, 2004.
DOI : 10.1007/s00373-003-0537-9

M. [. Ikhlef and . Rajabpour, Discrete holomorphic parafermions in the Ashkin???Teller model and SLE, Journal of Physics A: Mathematical and Theoretical, vol.44, issue.4, p.42001, 2011.
DOI : 10.1088/1751-8113/44/4/042001

M. [. Ishikawa and . Wakayama, Minor summation formulas of Pfaffians, survey and a new identity, Combinatorial methods in representation theory, pp.133-142, 1998.

P. W. Kasteleyn, The statistics of dimers on a lattice : I. the number of dimer arrangements on a quadratic lattice, pp.1209-1225, 1961.

]. P. Kas63 and . Kasteleyn, Dimer statistics and phase transitions, J. Math. Phys, vol.4, p.287, 1963.

]. P. Kas67 and . Kasteleyn, Graph theory and crystal physics, Graph Theory and Theoretical Physics, pp.43-110, 1967.

A. [. Kadanoff and . Brown, Correlation functions on the critical lines of the Baxter and Ashkin-Teller models, Annals of Physics, vol.121, issue.1-2, pp.318-342, 1979.
DOI : 10.1016/0003-4916(79)90100-3

L. P. Kadanoff and H. Ceva, Determination of an Operator Algebra for the Two-Dimensional Ising Model, Physical Review B, vol.3, issue.11, pp.3918-3939, 1971.
DOI : 10.1103/PhysRevB.3.3918

]. R. Ken97 and . Kenyon, Local statistics of lattice dimers, Ann. Inst. H. Poincaré Probab. Statist, vol.33, issue.5, pp.591-618, 1997.

]. R. Ken00 and . Kenyon, Conformal invariance of domino tiling, Ken01] R. Kenyon. Dominos and the Gaussian free field, pp.759-7951128, 2000.

R. Kenyon, The Laplacian and Dirac operators on critical planar graphs, Inventiones mathematicae, vol.150, issue.2, pp.409-439, 2002.
DOI : 10.1007/s00222-002-0249-4

R. Kenyon, Height Fluctuations in the Honeycomb Dimer Model, Communications in Mathematical Physics, vol.139, issue.3???4, pp.675-709, 2008.
DOI : 10.1007/s00220-008-0511-8

R. Kenyon, Spanning forests and the vector bundle Laplacian, The Annals of Probability, vol.39, issue.5, pp.1983-2017, 2011.
DOI : 10.1214/10-AOP596

G. Kirchhoff, Ueber die Aufl??sung der Gleichungen, auf welche man bei der Untersuchung der linearen Vertheilung galvanischer Str??me gef??hrt wird, Annalen der Physik und Chemie, vol.64, issue.12, pp.497-508, 1847.
DOI : 10.1002/andp.18471481202

R. Kenyon and A. Okounkov, Planar dimers and Harnack curves, Duke Mathematical Journal, vol.131, issue.3, pp.499-524, 2006.
DOI : 10.1215/S0012-7094-06-13134-4
URL : http://arxiv.org/abs/math/0311062

A. [. Kenyon, S. Okounkov, and . Sheffield, Dimers and amoebae, Annals of Mathematics, vol.163, issue.3, pp.1019-1056, 2006.
DOI : 10.4007/annals.2006.163.1019

G. Kuperberg, An exploration of the permanent-determinant method, Electron. J. Combin, vol.5, issue.1, p.46, 1998.

H. A. Kramers and G. H. Wannier, Statistics of the Two-Dimensional Ferromagnet. Part I, Physical Review, vol.60, issue.3, pp.252-262, 1941.
DOI : 10.1103/PhysRev.60.252

H. A. Kramers and G. H. Wannier, Statistics of the Two-Dimensional Ferromagnet. Part II, Physical Review, vol.60, issue.3, pp.263-276, 1941.
DOI : 10.1103/PhysRev.60.263

M. Kac and J. C. Ward, A Combinatorial Solution of the Two-Dimensional Ising Model, Physical Review, vol.88, issue.6, pp.1332-1337, 1952.
DOI : 10.1103/PhysRev.88.1332

F. [. Kadanoff and . Wegner, Some Critical Properties of the Eight-Vertex Model, Physical Review B, vol.4, issue.11, pp.3989-3993, 1971.
DOI : 10.1103/PhysRevB.4.3989

[. Li and S. Guo, Duality for the Ising model on a random lattice and topologic excitons, Nuclear Physics B, vol.413, issue.3, pp.723-734, 1994.
DOI : 10.1016/0550-3213(94)90009-4

]. Z. Li12 and . Li, Critical temperature of periodic Ising models, Comm. Math. Phys, vol.315, pp.337-381, 2012.

]. E. Lie67 and . Lieb, Residual entropy of square ice, Phys. Rev, vol.162, pp.162-172, 1967.

G. F. Lawler, O. Schramm, and W. Werner, Conformal Invariance Of Planar Loop-Erased Random Walks and Uniform Spanning Trees, Ann. Probab, vol.32, issue.1, pp.939-995, 2004.
DOI : 10.1007/978-1-4419-9675-6_30

]. R. Lyo98 and . Lyons, A bird's-eye view of uniform spanning trees and forests. Microsurveys in discrete probability, pp.135-162, 1998.

]. C. Mer01a and . Mercat, Discrete period matrices and related topics. ArXiv: math-ph/0111043, 2001.

C. Mercat, Discrete Riemann Surfaces and the Ising Model, Communications in Mathematical Physics, vol.218, issue.1, pp.177-216, 2001.
DOI : 10.1007/s002200000348
URL : https://hal.archives-ouvertes.fr/hal-00418532

R. Messikh, The surface tension near criticality of the 2d-ising model, Arxiv, p.610636, 2006.

]. C. Mon00 and . Monthus, On the localization of random heteropolymers at the interface between two selective solvents, Eur. Phys. J. B Condens. Matter Phys, vol.13, issue.1, pp.111-130, 2000.

G. Masbaum and A. Vaintrob, A new matrix-tree theorem, Int. Math. Res. Not, issue.27, pp.1397-1426, 2002.

B. Mccoy and F. Wu, The two-dimensional Ising model, 1973.

B. Nienhuis, Critical behavior of two-dimensional spin models and charge asymmetry in the Coulomb gas, Journal of Statistical Physics, vol.49, issue.FS3, pp.5-6731, 1984.
DOI : 10.1007/BF01009437

]. L. Ons44 and . Onsager, Crystal statistics. I. A two-dimensional model with an order-disorder transition, Phys. Rev, vol.65, issue.3-4, pp.117-149, 1944.

J. K. Percus, One More Technique for the Dimer Problem, Journal of Mathematical Physics, vol.10, issue.10, p.1881, 1969.
DOI : 10.1063/1.1664774

R. [. Picco and . Santachiara, Critical interfaces and duality in the Ashkin-Teller model, Physical Review E, vol.83, issue.6, p.61124, 2011.
DOI : 10.1103/PhysRevE.83.061124
URL : https://hal.archives-ouvertes.fr/hal-00533081

]. S. She05 and . Sheffield, Random surfaces, Astérisque, issue.304, p.175, 2005.

]. S. Smi01 and . Smirnov, Critical percolation in the plane: Conformal invariance, Cardy's formula, scaling limits, C. R. Acad. Sci. Paris Sér. I Math, vol.333, issue.3, pp.239-244, 2001.

]. S. Smi06 and . Smirnov, Towards conformal invariance of 2D lattice models, Proceedings of the ICM, pp.1421-1452, 2006.

]. S. Smi10 and . Smirnov, Conformal invariance in random cluster models. I. Holomorphic fermions in the Ising model, Ann. Math, vol.172, issue.2, pp.1435-1467, 2010.

]. B. Sut70 and . Sutherland, Two-dimensional hydrogen bonded crystals without the ice rule, J. Math. Phys, vol.11, issue.11, pp.3183-3186, 1970.

]. G. Tes00 and . Tesler, Matchings in graphs on non-orientable surfaces, J. Combin. Theory Ser. B, vol.78, issue.2, pp.198-231, 2000.

M. [. Temperley and . Fisher, Dimer problem in statistical mechanics-an exact result, Philosophical Magazine, vol.6, issue.68, pp.1061-1063, 1961.
DOI : 10.1039/df9531500057

]. W. Thu90 and . Thurston, Conway's tiling groups, Amer. Math. Monthly, vol.97, issue.8, pp.757-773, 1990.

]. F. Ton08 and . Toninelli, Disordered pinning models and copolymers: beyond annealed bounds, Ann. Appl. Probab, vol.18, issue.4, pp.1569-1587, 2008.

]. W. Tut48 and . Tutte, The dissection of equilateral triangles into equilateral triangles, Mathematical Proceedings of the Cambridge Philosophical Society, pp.463-482, 1948.

]. F. Weg72 and . Wegner, Duality relation between the Ashkin-Teller and the eight-vertex model, J. of Phys. C: Solid State Physics, vol.5, issue.11, p.131, 1972.

]. D. Wil11 and . Wilson, XOR-Ising loops and the Gaussian free field, 2011.

F. Y. Wu and K. Y. Lin, Staggered ice-rule vertex model???The Pfaffian solution, Physical Review B, vol.12, issue.1, pp.419-428, 1975.
DOI : 10.1103/PhysRevB.12.419

]. F. Wu71 and . Wu, Ising model with four-spin interactions, Phys. Rev. B, vol.4, pp.2312-2314, 1971.