General Griffiths' Inequalities on Correlations in Ising Ferromagnets

Abstract

Let N = (1, 2, ⋯, n). For each subset A of N, let JA ≥ 0. For eachi∈N, let σi ± 1. For each subset A of N, define σA=∏i∈A σi. Let the Hamiltonian be − ΣACN JA σA. Then for each A, B⊂N, 〈σA〉≥0 and 〈σAσB〉−〈σA〉〈σB〉≥0. This weakens the hypothesis and widens the conclusion of a result due to Griffiths.