Exact solution of the Maier-Saupe model for a nematic liquid crystal on a one-dimensional lattice

Abstract

The planar and spatial lattice versions of the Maier-Saupe model (1959, 1960) for a nematic liquid crystal are exactly solved for a one-dimensional lattice, without periodic boundary conditions. The two-molecule correlation functions are studied, and it is shown that these two models do not exhibit an order-disorder phase transition except at T=0, as is the case for the classical Heisenberg model in one dimension.