Lv, Jian-PingDeng, YoujinSalas Martínez, JesúsJacobsen, Jesper LykkeSokal, Alan2021-01-262021-01-262018-04-25Physical review E, 97(4), 040104(R), 5 pp.2470-00452470-0053 (online)https://doi.org/10.1103/PhysRevE.97.040104https://hdl.handle.net/10016/31784We 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.5eng© 2018 American Physical Societyresearch articleMatemáticasopen access14, 040104(R)5PHYSICAL REVIEW E97AR/0000021451