, Volume 80, Issue 2, pp 153-179

A general Lee-Yang theorem for one-component and multicomponent ferromagnets

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Abstract

We show that any measure on ℝ n possessing the Lee-Yang property retains that property when multiplied by a ferromagnetic pair interaction. Newman's Lee-Yang theorem for one-component ferromagnets with general single-spin measure is an immediate consequence. We also prove an analogous result for two-component ferromagnets. ForN-component ferromagnets (N ≧ 3), we prove a Lee-Yang theorem when the interaction is sufficiently anisotropic.