Phase transition for the dilute clock model

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

Stochastic Processes and their Applications, 2015, vol. 125, issue 10, 3879-3892

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.

Keywords: Dilute clock model; Phase transition (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1016/j.spa.2015.05.010

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