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

authors

  • Huang, Yuan
  • Chen, Kun
  • Deng, Youjin
  • JACOBSEN, JESPER LYKKE
  • Koteck√Ĺ, Roman
  • SALAS MARTINEZ, JESUS
  • SOKAL, ALAN D.
  • Swart, Jan M.

publication date

  • January 2013

start page

  • 012136

issue

  • 1

volume

  • 87

International Standard Serial Number (ISSN)

  • 1539-3755

Electronic International Standard Serial Number (EISSN)

  • 1550-2376

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.

keywords

  • square-lattice; monte-carlo; zero-temperature; models; representation; spin