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.