Tiles and Colors
Copyright policy )Tiles and Colors
Tiling models are classical statistical models in which different geometric shapes, the tiles, are packed together such that they cover space completely. In this paper we discuss a class of two-dimensional tiling models in which the tiles are rectangles and isosceles triangles. Some of these models have been solved recently by means of Bethe Ansatz. We discuss the question why only these models in a larger family are solvable, and we search for the Yang-Baxter structure behind their integrablity. In this quest we find the Bethe Ansatz solution of the problem of coloring the edges of the square lattice in four colors, such that edges of the same color never meet in the same vertex.
18 pages, 3 figures (in 5 eps files)
- University of Amsterdam Netherlands
random tiling, Nonlinear Sciences - Exactly Solvable and Integrable Systems, Statistical Mechanics (cond-mat.stat-mech), colorings, FOS: Physical sciences, 530, Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics, 004, integrable models, lattice models, Exactly Solvable and Integrable Systems (nlin.SI), Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics, quasicrystals, Statistical mechanics of crystals, Condensed Matter - Statistical Mechanics
random tiling, Nonlinear Sciences - Exactly Solvable and Integrable Systems, Statistical Mechanics (cond-mat.stat-mech), colorings, FOS: Physical sciences, 530, Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics, 004, integrable models, lattice models, Exactly Solvable and Integrable Systems (nlin.SI), Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics, quasicrystals, Statistical mechanics of crystals, Condensed Matter - Statistical Mechanics
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