A Note on First Order Phase Transitions in the Continuum

We consider the Potts model in R d , d ≥ 2 , with q ≥ 3 states and prove that for all values of the inverse temperature β which are small enough there is a critical value z c ( β ) of the fugacity so that at ( β , z c ( β ) ) there are q + 1 extremal DLR measures (thus the phase transition is of fir...

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Bibliographic Details
Published inJournal of statistical physics Vol. 162; no. 4; pp. 994 - 996
Main Authors Cassandro, M., Presutti, E.
Format Journal Article
LanguageEnglish
Published New York Springer US 01.02.2016
Springer
Subjects
Mathematical and Computational Physics
Physical Chemistry
Physics
Physics and Astronomy
Quantum Physics
Statistical Physics and Dynamical Systems
Theoretical
Large density limit
82B20
Potts model
60K35
Kac potentials
Phase transitions in the continuum
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Summary:We consider the Potts model in R d , d ≥ 2 , with q ≥ 3 states and prove that for all values of the inverse temperature β which are small enough there is a critical value z c ( β ) of the fugacity so that at ( β , z c ( β ) ) there are q + 1 extremal DLR measures (thus the phase transition is of first order). The first q have a spin which appears with higher frequency than the other spins while in the last one all the spins have the same frequency, moreover the particle density is strictly smaller than in the first q states.
ISSN:0022-4715
1572-9613
DOI:10.1007/s10955-015-1435-2