Communications in Mathematical Physics

, Volume 80, Issue 2, pp 153–179

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

  • Elliott H. Lieb
  • Alan D. Sokal

DOI: 10.1007/BF01213009

Cite this article as:
Lieb, E.H. & Sokal, A.D. Commun.Math. Phys. (1981) 80: 153. doi:10.1007/BF01213009


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. ForN-component ferromagnets (N ≧ 3), we prove a Lee-Yang theorem when the interaction is sufficiently anisotropic.

Copyright information

© Springer-Verlag 1981

Authors and Affiliations

  • Elliott H. Lieb
    • 1
  • Alan D. Sokal
    • 2
  1. 1.Departments of Mathematics and PhysicsPrinceton UniversityPrincetonUSA
  2. 2.Department of PhysicsPrinceton UniversityPrincetonUSA

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