Cluster Monte Carlo Simulations of the Nematic--Isotropic Transition

We report the results of simulations of the Lebwohl-Lasher model of the nematic-isotropic transition using a new cluster Monte Carlo algorithm. The algorithm is a modification of the Wolff algorithm for spin systems, and greatly reduces critical slowing down. We calculate the free energy in the neighborhood of the transition for systems up to linear size 70. We find a double well structure with a barrier that grows with increasing system size, obeying finite size scaling for systems of size greater than 35. We thus obtain an estimate of the value of the transition temperature in the thermodynamic limit.