TY - JOUR

T1 - Entropy-Driven Phase Transition in Low-Temperature Antiferromagnetic Potts Models

AU - Kotecký, Roman

AU - Sokal, Alan D.

AU - Swart, Jan M.

PY - 2014/9

Y1 - 2014/9

N2 - 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.

AB - 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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U2 - 10.1007/s00220-014-2005-1

DO - 10.1007/s00220-014-2005-1

M3 - Article

AN - SCOPUS:84903891784

SN - 0010-3616

VL - 330

SP - 1339

EP - 1394

JO - Communications In Mathematical Physics

JF - Communications In Mathematical Physics

IS - 3

ER -