Entropy-Driven Phase Transition in Low-Temperature Antiferromagnetic Potts Models

被引：0
作者：
Roman Kotecký
Alan D. Sokal
Jan M. Swart
机构：
[1] University of Warwick,Department of Mathematics
[2] Charles University,Center for Theoretical Study
[3] New York University,Department of Physics
[4] University College London,Department of Mathematics
[5] Institute of Information Theory and Automation of the ASCR (ÚTIA),undefined
来源：
Communications in Mathematical Physics | 2014年 / 330卷
关键词：
Planar Graph; Gibbs Measure; Simple Circuit; Graph Automorphism; Minimal Cutset;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We prove the existence of long-range order at sufficiently low temperatures, including zero temperature, for the three-state Potts antiferromagnet on a class of quasi-transitive plane quadrangulations, including the diced lattice. More precisely, we show the existence of (at least) three infinite-volume Gibbs measures, which exhibit spontaneous magnetization in the sense that vertices in one sublattice have a higher probability to be in one state than in either of the other two states. For the special case of the diced lattice, we give a good rigorous lower bound on this probability, based on computer-assisted calculations that are not available for the other lattices.
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页码：1339 / 1394
页数：55
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