The P₄ model and its orientational phase transition

Abstract

A simple generalization of the Lebwohl-Lasher model, where fourth rank, rather than second rank, interactions are involved is investigated. This model was first put forward and studied some years ago using molecular field theory (Zannoni, C., 1979, Molec. Crystals liq. Crystals Lett., 49, 247). There it was found that there should be a temperature interval where the fourth rank order parameter is higher than the second rank one. This unusual behaviour has been found by various groups to be consistent with fluorescence depolarization data for diphenylhexatriene in DPPC and DMPC membrane vesicles. In this paper we investigate more thoroughly the P ₄ model using Monte Carlo simulations with periodic boundary conditions on a 10 × 10 × 10 lattice and with the recently proposed Cluster Monte Carlo method on a 6 × 6 × 6 and a 10 × 10 × 10 lattice. Our results are consistent with a first order transition. We find that the results for the transition temperature and for the second and fourth rank order parameters are well approximated by two site cluster theory.