Nematic-Liquid-Crystal Order—A Monte Carlo Calculation

Abstract

The lattice version of the Maier-Saupe model of a nematic liquid crystal, in which all molecules are restricted to be on a simple-cubic lattice with periodic boundary conditions and to interact only with their nearest neighbors through the interaction energy ${E}_{\mathrm{ij}}=\ensuremath{-}\ensuremath{\epsilon}(\frac{3}{2}{{cos}^{2}\ensuremath{\theta}}_{\mathrm{ij}}\ensuremath{-}\frac{1}{2})$, is investigated using a Monte Carlo technique. The lattice is found to undergo a first-order phase transition at $\frac{\ensuremath{\epsilon}}{\mathrm{kT}}=0.890\ifmmode\pm\else\textpm\fi{}0.005$ with a spontaneous order of $〈{P}_{2}(cos\ensuremath{\theta})〉=0.33\ifmmode\pm\else\textpm\fi{}0.04$ at the transition.