PHASE UNIQUENESS AND CORRELATION LENGTH IN DILUTED-FIELD ISING-MODELS

The diluted-field Ising model, a random nonnegative field ferromagnetic model, is shown to have a unique Gibbs measure with probability 1 when the field mean is positive. Our methods involve comparisons with ordinary uniform field Ising models. They yield as a corollary a way of obtaining spontaneous magnetization through the application of a vanishing random magnetic field. The correlation lengths of this model defined as (lim(n) (-->) (infinity) - (1/n) log(sigma(0); sigma(n)))(-1), where n is the site on the first coordinate axis at distance it from the origin and (sigma(0); sigma(n)) is the origin to it two-point truncated correlation function, is non-random. We derive an upper bound for it in terms of the correlation length of an ordinary nonrandom model with uniform field related to the field distribution of the diluted model.