Thierry Gobron, Immacolata Merola
Phase transition induced by increasing the range of 
interaction in Potts Model
(216K, latex)

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.