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Communications in Mathematical Physics

, Volume 40, Issue 3, pp 283–308 | Cite as

Correlation inequalities for Ising spin lattices

  • J. K. Percus
Article

Abstract

A change of spin representation is used to present expectation inequalities on Ising lattices directly as sums of terms of like sign. The technique is extended to correlation inequalities by introducing replica variables which convert correlations into expectations on a larger space. Second order correlations are analyzed in full from this viewpoint, recovering the FKG set, among others. Third order correlations are examined in some detail, and the sign of the multi-site Ursell correlationsF3,F4,F6 established under appropriate restrictions.

Keywords

Neural Network Statistical Physic Complex System Nonlinear Dynamics Quantum Computing 
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Copyright information

© Springer-Verlag 1975

Authors and Affiliations

  • J. K. Percus
    • 1
  1. 1.Courant Institute of Mathematical Sciences and Physics DepartmentNew York UniversityNew YorkUSA

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