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Correlations in Ising ferromagnets. III

A mean-field bound for binary correlations

Abstract

An inequality relating binary correlation functions for an Ising model with purely ferromagnetic interactions is derived by elementary arguments and used to show that such a ferromagnet cannot exhibit a spontaneous magnetization at temperatures above the mean-field approximation to the Curie or “critical” point. (As a consequence, the corresponding “lattice gas” cannot undergo a first order phase transition in density (condensation) above this temperature.) The mean-field susceptibility in zero magnetic field at high temperatures is shown to be an upper bound for the exact result.

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Additional information

Research supported in part by the National Science Foundation.

Alfred P. Sloan research fellow.

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Griffiths, R.B. Correlations in Ising ferromagnets. III. Commun.Math. Phys. 6, 121–127 (1967). https://doi.org/10.1007/BF01654128

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Keywords

  • Magnetic Field
  • Neural Network
  • Phase Transition
  • Statistical Physic
  • Correlation Function