First-Order Phase Transition in Potts Models with finite-range interactionsReport as inadecuate

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1 LPTM - Laboratoire de Physique Théorique et Modélisation 2 Dipartimento di Matematica Pura e Applicata

Abstract : 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.

Keywords : Kac potentials Lebowitz-Penrose limit Pirogov-Sinai theory

Author: Thierry Gobron - Immacolata Merola -



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