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

TL;DR

This paper demonstrates that the $Q$-state Potts model with finite-range interactions exhibits a first-order phase transition for large potential ranges, contrasting with second-order transitions in nearest-neighbor cases.

Contribution

It proves the existence of a first-order phase transition in the Potts model with finite-range interactions using Pirogov-Sinai theory, showing a transition from second to first order by varying interaction range.

Findings

First-order phase transition for large finite-range interactions.

Coexistence of $Q+1$ Gibbs states at a specific temperature.

Contrasts with second-order transitions in nearest-neighbor models.

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.