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arXiv · 1210.6248

Two-dimensional Potts antiferromagnets with a phase transition at arbitrarily large q

Yuan Huang·Kun Chen·Youjin Deng·Jesper Lykke Jacobsen·Roman Kotecký·Jesús Salas·Alan D. Sokal·Jan M. Swart
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Abstract

We exhibit infinite families of two-dimensional lattices (some of which are triangulations or quadrangulations of the plane) on which the q-state Potts antiferromagnet has a finite-temperature phase transition at arbitrarily large values of q. This unexpected result is proven rigorously by using a Peierls argument to measure the entropic advantage of sublattice long-range order. Additional numerical data are obtained using transfer matrices, Monte Carlo simulation, and a high-precision graph-theoretic method.

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Yuan Huang, Kun Chen, Youjin Deng, Jesper Lykke Jacobsen, Roman Kotecký, Jesús Salas, Alan D. Sokal, Jan M. Swart. 2013-02-06. Two-dimensional Potts antiferromagnets with a phase transition at arbitrarily large q. https://doi.org/10.1103/physreve.87.012136

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