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Communications in Mathematical Physics

, Volume 330, Issue 3, pp 1339–1394 | Cite as

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

  • Roman KoteckýEmail author
  • Alan D. Sokal
  • Jan M. Swart
Article

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.

Keywords

Planar Graph Gibbs Measure Simple Circuit Graph Automorphism Minimal Cutset 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Roman Kotecký
    • 1
    • 2
    Email author
  • Alan D. Sokal
    • 3
    • 4
  • Jan M. Swart
    • 5
  1. 1.Department of MathematicsUniversity of WarwickCoventryUK
  2. 2.Center for Theoretical StudyCharles UniversityPragueCzech Republic
  3. 3.Department of PhysicsNew York UniversityNew YorkUSA
  4. 4.Department of MathematicsUniversity College LondonLondonUK
  5. 5.Institute of Information Theory and Automation of the ASCR (ÚTIA)Prague 8Czech Republic

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