Zero-one Laws for Binary Random Fields

A set of binary random variables indexed by a lattice torus is considered. Undera mixing hypothesis, the probability of any proposition belonging to the rst orderlogic of colored graphs tends to 0 or 1, as the size of the lattice tends to innity.For the particular case of the Ising model with bounded pair potential and surfacepotential tending to -1, the threshold functions of local propositions are computed,and sucient conditions for the zero-one law are given.