Monte-Carlo study of the Maier-Saupe model on square and triangle lattices

The Monte-Carlo method is used to investigate the statistical physics of the Maier-Saupe model on square and triangle lattices. These systems are found to exhibit higher than first order phase transitions except for the negative coupling square lattice case. The transition is signaled by a pronounced maximum in the specific heat as a function of temperature. The mechanism of the transition is shown to be associated with the onset of partial ordering of the vectors in individual members of the ensemble. A temperature dependent internal order parameter is introduced to characterize the degree of internal order in the system since the ordering process does not break the rotational symmetry of the Hamiltonian and no macroscopic order parameter exists.