Phase transition for the dilute clock model

2014/04/15 by Inés Armendáriz, Pablo A. Ferrari, Armendáriz, Inés +4
Mathematics · Physics and Astronomy · #Markov Chains and Monte Carlo Methods #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #math.PR

paper · pdf · doi:10.48550/arxiv.1404.4071

14 pages, 2 figures

arxiv created 2015/01/09 · arxiv updated 2015/01/12

Abstract

We prove that phase transition occurs in the dilute ferromagnetic nearest-neighbour q-state clock model in ℤ^d, 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.

Related

• Phase Transition in Long-Range q-state Models via Contours. Clock and Potts Models with Fields
• Phase transitions in q-state clock model
• Nonequilibrium phase transitions in a Brownian p-state clock model
• Kosterlitz-Thouless transition in planar spin models with bond dilution
• A new proof of the sharpness of the phase transition for Bernoulli percolation on \mathbb Z^d