One Dimensional Lattice Models of Plane Rotators

Abstract

The order-disorder properties of two one-dimensional lattice models of plane rotators are investigated. The first is a 256 particle-system and the anisotropic interaction is of the T ₂ (cos0_ij ) type (where T ₂ (cos0_ij ) is the second Tchebyshev polynomial cos 20_ij and 0_ij = 0_i - 0_j is the angle between molecular symmetry axes), confined to the nearest neighbours. In the other system the interaction is long-range, of the r ^−3/2 type, the anisotropic part being T₂(cos0_ij ) again. The system size is 512 with the range of interaction extending to 64-neighbours on each side. We have performed Monte Carlo studies of both systems and find that at low temperatures Faber's theory of nematic order accurately describes both systems. Comparison with the work of Romano⁸ reveals that for the system with long-range interaction, the transition temperature changes with the truncation distance of the potential.

Key Words:

• Lattice models
• monte carlo.