Wednesday, October 24, 2012

1210.6248 (Yuan Huang et al.)

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
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 result is proven rigorously using a Peierls argument. Additional numerical data are obtained using transfer matrices, Monte Carlo simulation, and a high-precision graph-theoretic method.
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