First-Order Phase Transition in Potts Models with Finite-Range Interactions

We consider the $Q$-state Potts model on $\mathbb Z^d$, $Q\ge 3$, $d\ge 2$, with Kac ferromagnetic interactions and scaling parameter $\ga$. We prove the existence of a first order phase transition for large but finite potential ranges. More precisely we prove that for $\ga$ small enough there is a...

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Bibliographic Details
Published in:Journal of statistical physics 2007-02, Vol.126 (3), p.507-583
Main Authors: Gobron, T., Merola, I.
Format: Article
Language:English
Subjects:
Mathematical Physics
Physics
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Summary:We consider the $Q$-state Potts model on $\mathbb Z^d$, $Q\ge 3$, $d\ge 2$, with Kac ferromagnetic interactions and scaling parameter $\ga$. We prove the existence of a first order phase transition for large but finite potential ranges. More precisely we prove that for $\ga$ small enough there is a value of the temperature at which coexist $Q+1$ Gibbs states. The proof is obtained by a perturbation around mean-field using Pirogov-Sinai theory. The result is valid in particular for $d=2$, $Q=3$, in contrast with the case of nearest-neighbor interactions for which available results indicate a second order phase transition. Putting both results together provides an example of a system which undergoes a transition from second to first order phase transition by changing only the finite range of the interaction.
ISSN:0022-4715
1572-9613
DOI:10.1007/s10955-006-9230-8