Abstract:We prove that a uniformly chosen proper 3-coloring of the d-dimensional discrete torus has a very rigid structure when the dimension d is sufficiently high. We show that with high probability the coloring takes just one color on almost all of either the even or the odd sub-torus. In particular, one color appears on nearly half of the torus sites. This model is the zero temperature case of the 3-state anti-ferromagnetic Potts model from statistical physics.Our work extends previously obtained results for the di… Show more
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