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Correlations in Ising ferromagnets. III

A mean-field bound for binary correlations


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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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).

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