CORRECTIONS TO THE CRITICAL-TEMPERATURE IN 2D ISING SYSTEMS WITH KAC POTENTIALS

We consider a d = 2 Ising system with a Kac potential whose mean-field critical temperature is 1. Calling gamma > 0 the Kac parameter, we pr ove that there exists c > 0 so that the true inverse critical tempera ture beta(cr)(gamma) > 1 + b gamma(2) log gamma(-1), for any b < c an d gamma correspondingly small. We also show that if gamma --> 0 and b --> c, suitably, then the correlation functions (normalized and resca led) converge to those of a non-Gaussian Euclidean field theory.