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

Elliott H. Lieb; Alan D. Sokal

doi:10.1007/BF01213009

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

Elliott H. Lieb, Alan D. Sokal

Mathematics

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101 Scopus citations

Abstract

We show that any measure on ℝⁿ 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. For N-component ferromagnets (N ≧ 3), we prove a Lee-Yang theorem when the interaction is sufficiently anisotropic.

Original language	English (US)
Pages (from-to)	153-179
Number of pages	27
Journal	Communications In Mathematical Physics
Volume	80
Issue number	2
DOIs	https://doi.org/10.1007/BF01213009
State	Published - Jun 1981

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/BF01213009

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abstract = "We show that any measure on ℝn 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. For N-component ferromagnets (N ≧ 3), we prove a Lee-Yang theorem when the interaction is sufficiently anisotropic.",

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AB - We show that any measure on ℝn 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. For N-component ferromagnets (N ≧ 3), we prove a Lee-Yang theorem when the interaction is sufficiently anisotropic.

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

Abstract

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