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Entropy-driven phase transition in low-temperature antiferromagnetic Potts models
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Kotecky, Roman, Sokal, Alan D. and Swart, Jan M. (2014) Entropy-driven phase transition in low-temperature antiferromagnetic Potts models. Communications in Mathematical Physics, Volume 330 (Number 3). pp. 1339-1394. doi:10.1007/s00220-014-2005-1 ISSN 0010-3616.
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Official URL: http://dx.doi.org/10.1007/s00220-014-2005-1
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.
Item Type: | Journal Article | ||||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||
Journal or Publication Title: | Communications in Mathematical Physics | ||||||
Publisher: | Springer | ||||||
ISSN: | 0010-3616 | ||||||
Official Date: | September 2014 | ||||||
Dates: |
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Volume: | Volume 330 | ||||||
Number: | Number 3 | ||||||
Page Range: | pp. 1339-1394 | ||||||
DOI: | 10.1007/s00220-014-2005-1 | ||||||
Status: | Peer Reviewed | ||||||
Publication Status: | Published | ||||||
Access rights to Published version: | Restricted or Subscription Access |
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