91-28 Fontes L.R.G.

An Ordered Phase with Slow Decay of Correlations in Continuum 1/r^2 Ising Models (45K, LaTeX) Sep 18, 91

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Abstract. For continuum 1/r^2 Ising models, we prove that the critical value of the long range coupling constant (inverse temperature), above which an ordered phase occurs (for strong short range cut- off), is exactly 1. This leads to a proof of the existence of an ordered phase with slow decay of correlations. Our arguments in- volve comparisons between continuum and discrete Ising models, including (quenched and annealed) site diluted models, which may be of independent interest.

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