Phase diagram for the bisected-hexagonal-lattice five-state Potts antiferromagnet Articles uri icon

publication date

  • September 2020

start page

  • 1

end page

  • 23


  • 3, 032124


  • 102

International Standard Serial Number (ISSN)

  • 2470-0045

Electronic International Standard Serial Number (EISSN)

  • 2470-0053


  • In this paper we study the phase diagram of the five-state Potts antiferromagnet on the bisected-hexagonal lattice. This question is important since Delfino and Tartaglia recently showed that a second-order transition in a five-state Potts antiferromagnet is allowed, and the bisected-hexagonal lattice had emerged as a candidate for such a transition on numerical grounds. By using high-precision Monte Carlo simulations and two complementary analysis methods, we conclude that there is a finite-temperature first-order transition point. This one separates a paramagnetic high-temperature phase, and a low-temperature phase where five phases coexist. This phase transition is very weak in the sense that its latent heat (per edge) is two orders of magnitude smaller than that of other well-known weak first-order phase transitions.


  • Mathematics


  • partition-function zeros; dynamic critical-behavior; first-order transition points; swendsen-wang algorithm; random-cluster model; transfer-matrices; square-lattice; chromatic polynomials; kempe equivalence; ising-model