RT Journal Article
T1 The three-state Potts antiferromagnet on plane quadrangulations
A1 Lv, Jian-Ping
A1 Deng, Youjin
A1 Jacobsen, Jesper L.
A1 Salas Martínez, Jesús
AB We study the antiferromagnetic 3-state Potts model on general (periodic) plane quadrangulations Gamma. Any quadrangulation can be built from a dual pair (G,G*). Based on the duality properties of G, we propose a new criterion to predict the phase diagram of this model. If Gamma is of self-dual type (i.e. if G is isomorphic to its dual G*), the model has a zero-temperature critical point with central charge c = 1, and it is disordered at all positive temperatures. If Gamma is of non-self-dual type (i.e. if G is not isomorphic to G*), three ordered phases coexist at low temperature, and the model is disordered at high temperature. In addition, there is a finite-temperature critical point (separating these two phases) which belongs to the universality class of the ferromagnetic 3-state Potts model with central charge c = 4 / 5. We have checked these conjectures by studying four (resp. seven) quadrangulations of self-dual (resp. non-self-dual) type, and using three complementary high-precision techniques: Monte-Carlo simulations, transfer matrices, and critical polynomials. In all cases, we find agreement with the conjecture. We have also found that the Wang-Swendsen-Kotecky Monte Carlo algorithm does not have (resp. does have) critical slowing down at the corresponding critical point on quadrangulations of self-dual (resp. non-self-dual) type.
PB IOP Publishing Ltd.
SN 1751-8113
SN 1751-8121 (online)
YR 2018
FD 2018-07-21
LK https://hdl.handle.net/10016/31795
UL https://hdl.handle.net/10016/31795
LA eng
NO This work has been supported in part by the National Natural Science Foundation of China under grants No. 11774002 (JPL), and No. 11625522 (YD), the Key Projects of Anhui Province University Outstanding Youth Talent Support Program grant gxyqZD2017009 (JPL), the Ministry of Science and Technology of China grant No. 2016YFA0301600 (YD), the Institut Universitaire de France, and the European Research Council through the Advanced Grant NuQFT (JLJ), and the MINECO FIS2014-57387-C3-3-P and MINECO/AEI/FEDER, UE FIS2017-84440-C2-2-P grants (JLJ and JS).
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RD 1 may. 2024