A Monte Carlo Calculation of the Nematic-Isotropic Phase Transition

Abstract

The behaviour of a lattice version of the Maier-Saupe model near the clearing point is investigated using a biased Monte Carlo technique. The lattice version consists of an array of unit vectors, which are located at the sites of a n x n x n (n = 14, 16, 18, 20) simple-cubic lattice with periodic boundary conditions and interact by way of a nearest neighbour coupling. The system undergoes a first order phase transition with a spontaneous order S = 0.333 ± 0.009 at the clearing temperature T_c given by β_cϵ = 0.894 ± 0.001, where ϵ denotes the maximum interaction energy between two nearest neighbours. The pretransitional light scattering in the isotropic phase can be reasonably well described by [T - T_c*]⁻¹, with (T_c - T_c= 0.009 ± 0.007 for n = 14 and (T_c - T_c*)/T_c = 0.007 ± 0.004 for n = 16. This type of divergence is in agreement with experiment.