Closed-form solutions and free energy of hard-spin mean-field theory of a fully frustrated system

Abstract

Closed-form solutions of the hard-spin mean-field theory equations for the antiferromagnetic Ising model on a triangular lattice, with or without an external field H, are obtained, showing the lack of order for H=0 and very good agreement with Monte Carlo data for the onset of order for nonzero H. A free energy calculation is developed, within the context of hard-spin mean-field theory, distinguishing between metastable solutions and true thermodynamic equilibrium. © 1994 The American Physical Society.