Cassandro, R., Marra R., Presutti, E.
Corrections to the critical temperature 
in 2d Ising systems with Kac potentials
(23K, TeX)

ABSTRACT.  We consider a $d=2$ Ising system with a Kac
potential whose mean field critical temperature is 1. 
Calling  $\gam>0$ the Kac parameter,  we prove that
there exists $c^\star>0$ so that the true
inverse critical temperature $\beta_{\text{cr}}(\gam)> 1 + b
\gam^2\log\gam^{-1}$, for any $b<c^\star$ and $\gam$
correspondingly small.  We also show that  if
$\gam\to 0$ and $b\to c^\star$, suitably, then the 
correlation functions (normalized
and rescaled) converge to those of a non trivial
Euclidean field theory.