First-Order Phase Transition in Potts Models with finite-range interactions

Details First-Order Phase Transition in Potts Models with finite-range interactions First-Order Phase Transition in Potts Models with finite-range interactions

2006-09-18

arxiv.org/abs/math-ph/0609051v1

Journal of Statistical Physics 126, 3 (2007) pages 507-583

Physics

Mathematical Physics

Soumis pour publication a Journal of statistical physics - version r\'{e}vis\'{e}e

Scientific paper

10.1007/s10955-006-9230-8

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.

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