Phase transition for the dilute clock model

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 percola...

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Detalles Bibliográficos
Autores principales: Armendáriz, I., Ferrari, P.A., Soprano-Loto, N.
Formato: JOUR
Materias:
Dilute clock model
Phase transition
Clocks
Percolation (solid state)
Phase transitions
Solvents
Bernoulli
Bond percolation
Clock model
Low temperatures
Nearest neighbour
Q state
Random-cluster representations
Supercritical
Potts model
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_03044149_v125_n10_p3879_Armendariz
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
Descripción
Sumario: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. © 2015 Elsevier B.V. All rights reserved.

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