Monte Carlo simulation of a planar lattice model with P4 interactions

Monte Carlo study of a two-dimensional lattice with three-dimensional spins (d=2,n=3) interacting with nearest neighbors via a -P4(cos theta) potential, where P4 is the fourth Legendre polynomial and theta is the angle between two spins, has been reported for lattice sizes ranging from 10 x 10 to 160 x 160. A cluster algorithm for spin updating with a histogram reweighting technique has been used and finite size scaling has been performed. The model exhibits a strong first order phase transition at a dimensionless temperature 0.376+/-0.015. The phase transition appears to be driven by condensation of topological defects and the defect density D increases sharply at the transition temperature. The temperature derivative dD/dT* is found to obey a linear scaling relation with the lattice size L. The behavior of the model seems to be remarkably different from the two-dimensional P2 model, that has been investigated by other authors, although both models possess the same symmetry and topological defects play an important role in the phase transition.