Decay of Correlations in Ferromagnets

Abstract

Some new correlation inequalities are described which bound large-distance behavior of correlations in ferromagnets from above by correlations at intermediate distances. Among applications are (1) an inequality, η < 1, on the decay of correlations at the critical point; (2) an inequality χ ≧ coth(1/2 m) relating the zero-field susceptibility and the mass gap in a nearest-neighbor ferromagnet; (3) a finite algorithm for rigorously computing a sequence of upper bounds guaranteed to converge to the true transition temperature in Ising ferromagnets.

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