Study of an anisotropic lattice model with interactions of rank higher than four

Abstract

We have considered a classical system, consisting of cylindrically symmetric particles, associated with a three-dimensional, simple cubic lattice, and interacting via nearest neighbour pair potentials of the form

here P _L is a Legendre polynomial of order L, ε is a positive constant setting the temperature and energy scales, and u _j and u _k denote the unit vectors defining particle orientations. These potential models have been studied previously in the literature by means of molecular field theory; we report here two-site cluster results for L = 6,8 and Monte Carlo simulation results for L = 6. Comparison shows that the two-site cluster approximation produces an overall qualitative improvement over molecular field theory.