Two-dimensional Potts antiferromagnets with a phase transition at   arbitrarily large q
  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. 
Yuan Huang, Kun Chen, Youjin Deng, Jesper Lykke Jacobsen, Roman   Koteck\'y, Jes\'us Salas, Alan D. Sokal, Jan M. Swart
cond-mat.stat-mech math-ph math.MP