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Phase transition for the dilute clock model

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  • Armendáriz, Inés
  • Ferrari, Pablo A.
  • Soprano-Loto, Nahuel

Abstract

We prove that phase transition occurs in the dilute ferromagnetic nearest-neighbour q-state clock model in Zd, for every q≥2 and d≥2. This follows from the fact that the Edwards–Sokal random-cluster representation of the clock model stochastically dominates a supercritical Bernoulli bond percolation probability, a technique that has been applied to show phase transition for the low-temperature Potts model. The domination involves a combinatorial lemma which is one of the main points of this article.

Suggested Citation

  • Armendáriz, Inés & Ferrari, Pablo A. & Soprano-Loto, Nahuel, 2015. "Phase transition for the dilute clock model," Stochastic Processes and their Applications, Elsevier, vol. 125(10), pages 3879-3892.
    • Handle: RePEc:eee:spapps:v:125:y:2015:i:10:p:3879-3892
    DOI: 10.1016/j.spa.2015.05.010
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    Keywords

    Dilute clock model; Phase transition;

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