Lv, JP; Deng, Y; Jacobsen, JL; Salas, J; Sokal, AD; (2018) Duality and the universality class of the three-state Potts antiferromagnet on plane quadrangulations. [Rapid communication]. Physical Review E , 97 (4) 10.1103/PhysRevE.97.040104.

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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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