Duality and the universality class of the three-state Potts antiferromagnet on plane quadrangulations. Articles uri icon

publication date

  • April 2018

start page

  • 1

end page

  • 5

issue

  • 4, 040104 R

volume

  • 97

International Standard Serial Number (ISSN)

  • 2470-0053

Electronic International Standard Serial Number (EISSN)

  • 2470-0045

abstract

  • We provide a criterion based on graph duality to predict whether the three-state Potts antiferromagnet on a plane quadrangulation has a zero-or finite-temperature critical point, and its universality class. The former case occurs for quadrangulations of self-dual type, and the zero-temperature critical point has central charge c = 1. The latter case occurs for quadrangulations of non-self-dual type, and the critical point belongs to the universality class of the three-state Potts ferromagnet. We have tested this criterion against high-precision computations on four lattices of each type, with very good agreement. We have also found that the Wang-Swendsen-Kotecky algorithm has no critical slowing-down in the former case, and critical slowing-down in the latter.

subjects

  • Mathematics