05-272 Thierry Gobron, Immacolata Merola
Phase transition induced by increasing the range of interaction in Potts Model (216K, latex) Aug 10, 05
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Abstract. We consider the $Q$-state Potts model on $\mathbb Z^d$, $Q\ge 3$, $d\ge 2$, with a Kac ferromagnetic interaction, with scaling parameter $\ga$. When $\ga \to 0$ the range increases as $\ga^{-1}$ and the ``strength" remains equal to $1$. We prove the existence of a first order phase transition for $\ga$ small enough (thus with potential range finite). The proof is obtained by a perturbation around mean-field using the Pirogov-Sinai theory. The result is valid in particular for $d=2$, $Q=3$, thus providing an example of a system which undergoes a transition from second to first order phase transition when varying the finite range of the interaction.

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