Generalized Mean-Field Equations with Application to Nematic-Isotropic Transitions

Abstract

The mean-field equations are derived for a system whose energy depends arbitrarily on any number of continuous order-parameters. The results are applied to a non-linear one-order-parameter model of nematic liquid crystals, exhibiting an improvement over the Maier-Saupe model similar to that previously obtained using a two-order-parameter model.