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Duality and the universality class of the three-state Potts antiferromagnet on plane quadrangulations
2018-06-28
Phys. Rev. E 97(4):40104 Apr 2018

Lv, Jian-Ping; Deng, Youjin; Jacobsen, Jesper Lykke; Salas, Jesus; Sokal, Alan D.

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-Kotecký algorithm has no critical slowing-down in the former case, and critical slowing-down in the latter.

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