D. Aldous, Random walks on finite groups and rapidly mixing Markov chains Séminaire de Probabilités XVII, Lecture Notes in Mathematics, vol.82, issue.986, pp.243-297, 1981.

H. Van-beijeren, Exactly Solvable Model for the Roughening Transition of a Crystal Surface, Physical Review Letters, vol.38, issue.18, pp.993-996, 1977.
DOI : 10.1103/PhysRevLett.38.993

R. Berger, The undecidability of the domino problem Memoirs Amer, Math. Soc, vol.66, pp.1-72, 1966.

H. W. Blöte and H. J. Hilhorst, Roughening transitions and the zero-temperature triangular Ising antiferromagnet, Journal of Physics A: Mathematical and General, vol.15, issue.11, pp.631-637, 1982.
DOI : 10.1088/0305-4470/15/11/011

J. K. Burton, J. , and C. L. Henley, A constrained Potts antiferromagnet model with an interface representation, Journal of Physics A: Mathematical and General, vol.30, issue.24, pp.8385-8413, 1997.
DOI : 10.1088/0305-4470/30/24/007

H. Cohn, R. Kenyon, and J. 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

H. Cohn, M. Larsen, and J. Propp, The shape of a typical boxed plane partition, New York J. Math, vol.4, pp.137-165, 1998.

J. H. Conway and J. C. Lagarias, Tiling with polyominoes and combinatorial group theory, Journal of Combinatorial Theory, Series A, vol.53, issue.2, pp.183-206, 1990.
DOI : 10.1016/0097-3165(90)90057-4

N. Destainville, Flip Dynamics in Octagonal Rhombus Tiling Sets, Physical Review Letters, vol.88, issue.3
DOI : 10.1103/PhysRevLett.88.030601

URL : https://hal.archives-ouvertes.fr/hal-00003397

N. Destainville, R. Mosseri, and F. Bailly, Fixed-boundary octagonal random tilings: a combinatorial approach, Journal of Statistical Physics, vol.102, issue.1/2, pp.147-190, 2001.
DOI : 10.1023/A:1026564710037

N. Destainville, R. Mosseri, and F. Bailly, Configurational entropy of codimension-one tilings and directed membranes, Journal of Statistical Physics, vol.10, issue.1, p.697, 1997.
DOI : 10.1007/BF02181243

P. Diaconis and L. Saloff-coste, Comparison Theorems for Reversible Markov Chains, The Annals of Applied Probability, vol.3, issue.3, pp.696-730, 1993.
DOI : 10.1214/aoap/1177005359

S. Elnitsky, Rhombic Tilings of Polygons and Classes of Reduced Words in Coxeter Groups, Journal of Combinatorial Theory, Series A, vol.77, issue.2, pp.193-221, 1997.
DOI : 10.1006/jcta.1997.2723

M. E. Fisher, Statistical Mechanics of Dimers on a Plane Lattice, Physical Review, vol.124, issue.6, pp.1664-1672, 1961.
DOI : 10.1103/PhysRev.124.1664

M. E. Fisher and J. Stephenson, Statistical Mechanics of Dimers on a Plane Lattice. II. Dimer Correlations and Monomers, Physical Review, vol.132, issue.4, pp.1411-1431, 1963.
DOI : 10.1103/PhysRev.132.1411

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

C. Henley, Relaxation time for a dimer covering with height representation, Journal of Statistical Physics, vol.70, issue.3-4, pp.483-507, 1997.
DOI : 10.1007/BF02765532

D. A. Huse and A. D. Rutenberg, Classical antiferromagnets on the Kagom?? lattice, Physical Review B, vol.45, issue.13, pp.7536-7539, 1992.
DOI : 10.1103/PhysRevB.45.7536

W. Jockusch, J. Propp, and P. Shor, Random domino tilings and the arctic circle theorem

P. W. Kasteleyn, The statistics of dimers on a lattice, Physica, vol.27, issue.12, pp.1209-1225, 1961.
DOI : 10.1016/0031-8914(61)90063-5

C. Kenyon and R. Kenyon, Tiling a polygon with rectangles, Proceedings., 33rd Annual Symposium on Foundations of Computer Science, pp.610-619, 1992.
DOI : 10.1109/SFCS.1992.267790

R. Kenyon, Tiling a polygon with parallelograms, Algorithmica, vol.12, issue.4, pp.382-397, 1993.
DOI : 10.1007/BF01228510

R. Kenyon, Dominos and the Gaussian Free Field, The Annals of Probability, vol.29, issue.3
DOI : 10.1214/aop/1015345599

R. Kenyon, Local statistics of lattice dimers, Annales de l'Institut Henri Poincare (B) Probability and Statistics, vol.33, issue.5
DOI : 10.1016/S0246-0203(97)80106-9

J. Kolafa, Monte Carlo study of the three-state square Potts antiferromagnet, Journal of Physics A: Mathematical and General, vol.17, issue.14, pp.777-781, 1984.
DOI : 10.1088/0305-4470/17/14/010

J. Kondev and C. L. Henley, Four-coloring model on the square lattice: A critical ground state, Physical Review B, vol.52, issue.9, pp.6628-6639, 1995.
DOI : 10.1103/PhysRevB.52.6628

H. J. Knops, Renormalization connection between the eight-vertex model and the gaussian model, Annals of Physics, vol.128, issue.2, pp.448-462, 1981.
DOI : 10.1016/0003-4916(80)90328-0

J. C. Lagarias and D. S. Romano, A polyomino tiling problem of Thurston and its configurational entropy, Journal of Combinatorial Theory, Series A, vol.63, issue.2, pp.338-358, 1993.
DOI : 10.1016/0097-3165(93)90065-G

L. S. Levitov, Equivalence of the dimer resonating-valence-bond problem to the quantum roughening problem, Physical Review Letters, vol.64, issue.1, pp.92-94, 1990.
DOI : 10.1103/PhysRevLett.64.92

H. Lewis, Complexity of solvable cases of the decision problem for the predicate calculus, 19th Annual Symposium on Foundations of Computer Science (sfcs 1978), pp.35-47, 1978.
DOI : 10.1109/SFCS.1978.9

M. Luby, D. Randall, and A. Sinclair, Markov chain algorithms for planar lattice structures, Proc. 36th Symposium on Foundations of Computer Science, pp.150-159, 1995.

C. Moore, M. G. Nordahl, N. Minar, and C. Shalizi, Vortex dynamics and entropic forces in antiferromagnets and antiferromagnetic Potts models, Physical Review E, vol.60, issue.5, pp.5344-5351, 1999.
DOI : 10.1103/PhysRevE.60.5344

C. Moore and M. E. Newman, Height representation, critical exponents, and ergodicity in the four-state triangular Potts antiferromagnet, Journal of Statistical Physics, vol.99, issue.3/4, pp.661-690, 2000.
DOI : 10.1023/A:1018627008925

C. Moore and I. Pak, Ribbon Tile Invariants from the Signed Area, Journal of Combinatorial Theory, Series A, vol.98, issue.1
DOI : 10.1006/jcta.2001.3208

C. Moore and J. M. Robson, Hard Tiling Problems with Simple Tiles, Discrete & Computational Geometry, vol.26, issue.4
DOI : 10.1007/s00454-001-0047-6

C. Moore, Height representation and long-range order in random trimer tilings of the square lattice

M. E. Newman and G. T. Barkema, Monte Carlo Methods in Statistical Physics, 1999.

B. Nienhuis, H. J. Hilhorst, and H. W. Blöte, Triangular SOS models and cubic-crystal shapes, Journal of Physics A: Mathematical and General, vol.17, issue.18, pp.3559-3581, 1984.
DOI : 10.1088/0305-4470/17/18/025

J. Propp and D. Wilson, Exact sampling with coupled Markov chains and applications to statistical mechanics, Random Structures and Algorithms, vol.9, issue.1-2, pp.223-252, 1996.
DOI : 10.1002/(SICI)1098-2418(199608/09)9:1/2<223::AID-RSA14>3.0.CO;2-O

R. Raghavan, C. L. Henley, and S. L. Arouh, New two-color dimer models with critical ground states, Journal of Statistical Physics, vol.38, issue.3-4, pp.517-550, 1997.
DOI : 10.1007/BF02199112

URL : http://arxiv.org/abs/cond-mat/9606220

D. Randall and P. Tetali, Analyzing Glauber dynamics by comparison of Markov chains, Journal of Mathematical Physics, vol.41, issue.3, pp.1598-1615, 2000.
DOI : 10.1063/1.533199

D. Randall and G. Yngve, Random three-dimensional tilings of Aztec octahedra and tetrahedra: an extension of domino tilings, Proc. 11th Symp. on Discrete Algorithms, 2000.

E. Rémila, Tiling groups: New applications in the triangular lattice, Discrete & Computational Geometry, vol.14, issue.2, pp.189-204, 1998.
DOI : 10.1007/PL00009382

R. M. Robinson, Undecidability and nonperiodicity for tilings of the plane, Inventiones Mathematicae, vol.40, issue.3, p.177, 1971.
DOI : 10.1007/BF01418780

W. P. Thurston, Conway's Tiling Groups, The American Mathematical Monthly, vol.97, issue.8, pp.757-773, 1990.
DOI : 10.2307/2324578

J. Wang, R. H. Swendsen, and R. Koteck´ykoteck´y, Antiferromagnetic Potts models, Physical Review Letters, vol.63, issue.2, pp.109-112, 1989.
DOI : 10.1103/PhysRevLett.63.109

D. Wilson, Exact Sampling with Markov Chains, 1996.

D. Wilson, Mixing times of lozenge tiling and card shuffling Markov chains, The Annals of Applied Probability, vol.14, issue.1
DOI : 10.1214/aoap/1075828054

C. Zeng and P. L. Leath, Application of polynomial algorithms to a random elastic medium Absence of two-dimensional Bragg glasses, p.9807281

W. Zheng and S. Sachdev, Sine-Gordon theory of the non-N??el phase of two-dimensional quantum antiferromagnets, Physical Review B, vol.40, issue.4, pp.2704-2707, 1989.
DOI : 10.1103/PhysRevB.40.2704