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. ,
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
The undecidability of the domino problem Memoirs Amer, Math. Soc, vol.66, pp.1-72, 1966. ,
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
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
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
The shape of a typical boxed plane partition, New York J. Math, vol.4, pp.137-165, 1998. ,
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
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
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
Configurational entropy of codimension-one tilings and directed membranes, Journal of Statistical Physics, vol.10, issue.1, p.697, 1997. ,
DOI : 10.1007/BF02181243
Comparison Theorems for Reversible Markov Chains, The Annals of Applied Probability, vol.3, issue.3, pp.696-730, 1993. ,
DOI : 10.1214/aoap/1177005359
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
Statistical Mechanics of Dimers on a Plane Lattice, Physical Review, vol.124, issue.6, pp.1664-1672, 1961. ,
DOI : 10.1103/PhysRev.124.1664
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
Dimer problem in statistical mechanics-an exact result, Philosophical Magazine, vol.6, issue.68, pp.1061-1063, 1961. ,
DOI : 10.1039/df9531500057
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
Classical antiferromagnets on the Kagom?? lattice, Physical Review B, vol.45, issue.13, pp.7536-7539, 1992. ,
DOI : 10.1103/PhysRevB.45.7536
Random domino tilings and the arctic circle theorem ,
The statistics of dimers on a lattice, Physica, vol.27, issue.12, pp.1209-1225, 1961. ,
DOI : 10.1016/0031-8914(61)90063-5
Tiling a polygon with rectangles, Proceedings., 33rd Annual Symposium on Foundations of Computer Science, pp.610-619, 1992. ,
DOI : 10.1109/SFCS.1992.267790
Tiling a polygon with parallelograms, Algorithmica, vol.12, issue.4, pp.382-397, 1993. ,
DOI : 10.1007/BF01228510
Dominos and the Gaussian Free Field, The Annals of Probability, vol.29, issue.3 ,
DOI : 10.1214/aop/1015345599
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
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
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
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
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
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
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
Markov chain algorithms for planar lattice structures, Proc. 36th Symposium on Foundations of Computer Science, pp.150-159, 1995. ,
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
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
Ribbon Tile Invariants from the Signed Area, Journal of Combinatorial Theory, Series A, vol.98, issue.1 ,
DOI : 10.1006/jcta.2001.3208
Hard Tiling Problems with Simple Tiles, Discrete & Computational Geometry, vol.26, issue.4 ,
DOI : 10.1007/s00454-001-0047-6
Height representation and long-range order in random trimer tilings of the square lattice ,
Monte Carlo Methods in Statistical Physics, 1999. ,
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
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
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
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
Random three-dimensional tilings of Aztec octahedra and tetrahedra: an extension of domino tilings, Proc. 11th Symp. on Discrete Algorithms, 2000. ,
Tiling groups: New applications in the triangular lattice, Discrete & Computational Geometry, vol.14, issue.2, pp.189-204, 1998. ,
DOI : 10.1007/PL00009382
Undecidability and nonperiodicity for tilings of the plane, Inventiones Mathematicae, vol.40, issue.3, p.177, 1971. ,
DOI : 10.1007/BF01418780
Conway's Tiling Groups, The American Mathematical Monthly, vol.97, issue.8, pp.757-773, 1990. ,
DOI : 10.2307/2324578
Antiferromagnetic Potts models, Physical Review Letters, vol.63, issue.2, pp.109-112, 1989. ,
DOI : 10.1103/PhysRevLett.63.109
Exact Sampling with Markov Chains, 1996. ,
Mixing times of lozenge tiling and card shuffling Markov chains, The Annals of Applied Probability, vol.14, issue.1 ,
DOI : 10.1214/aoap/1075828054
Application of polynomial algorithms to a random elastic medium Absence of two-dimensional Bragg glasses, p.9807281 ,
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