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

Date: 2013-01-24
Authors Yuan Huang, Kun Chen, Youjin Deng, Jesper Lykke Jacobsen, Roman Kotecký, Jesús Salas, Alan D. Sokal, and Jan M. Swart
Journal No. Phys. Rev. E 87, 012136 (2013)
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.