Kotecky, R;
Sokal, AD;
Swart, JM;
(2014)
Entropy-Driven Phase Transition in Low-Temperature Antiferromagnetic Potts Models.
Communications in Mathematical Physics
, 330
(3)
pp. 1339-1394.
10.1007/s00220-014-2005-1.
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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.
| Type: | Article |
|---|---|
| Title: | Entropy-Driven Phase Transition in Low-Temperature Antiferromagnetic Potts Models |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1007/s00220-014-2005-1 |
| Publisher version: | https://doi.org/10.1007/s00220-014-2005-1 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10101898 |
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