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


publication date

  • June 2013

start page

  • 1

end page

  • 5


  • 1(012136)


  • 87

International Standard Serial Number (ISSN)

  • 1539-3755

Electronic International Standard Serial Number (EISSN)

  • 1550-2376


  • 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.


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