Study Of A Planar Lattice Model With $P_4$ Interaction

A planar square lattice model with 3-d spins interacting with nearest neighbours through a potential -$\epsilon P_4 (cos \theta_{ij})$ is studied by Monte Carlo technique. Lattice sizes from 10$\times$10 to 30$\times$30 are considered for calculating various thermodynamic averages. A 80$\times$80 lattice has been used to obtain the pair correlation function. To accurately ascertain the order of the phase transition the Ferrenberg-Swendsen technique has been used on a 120$\times$120 lattice. Our study predicts that the system exhibits a first order phase transition which is confirmed by the twin-peaked nature of the distribution function. The pair correlation function shows an algebraic decay at low temperatures and an exponential decay at high temperatures. Mean field and Two-site Cluster calculations have also been performed and the latter is found to predict the thermodynamic averages fairly accurately.