  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.
