Abstract
The diluted-field Ising model, a random nonnegative field ferromagnetic model, is shown to have a unique Gibbs measure with probability I 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→∞-(1/n) log 〈δ0;δ n〉)-1, wheren is the site on the first coordinate axis at distancen from the origin and 〈δ0;δ n 〉 is the origin ton 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.
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Fontes, L.R.G., Neves, E.J. Phase uniqueness and correlation length in diluted-field Ising models. J Stat Phys 80, 1327–1339 (1995). https://doi.org/10.1007/BF02179873
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DOI: https://doi.org/10.1007/BF02179873