Entropy-driven phase transition in low-temperature antiferromagnetic Potts models
Abstract
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.
Cite
@article{arxiv.1205.4472,
title = {Entropy-driven phase transition in low-temperature antiferromagnetic Potts models},
author = {Roman Kotecký and Alan D. Sokal and Jan M. Swart},
journal= {arXiv preprint arXiv:1205.4472},
year = {2014}
}
Comments
LaTeX2e, 67 pages. Version 3 is the final version, accepted for publication in Communications in Mathematical Physics