MICROCANONICAL MONTE-CARLO STUDY OF A 2-DIMENSIONAL BLUME-CAPEL MODEL

A microcanonical Monte Carlo algorithm has been developed to calculate the density of states of a two-dimensional Blume-Capel model in zero field. The full density of states is calculated for a 16 x 16 lattice as a function of the two spin summations which appear in the Hamiltonian. This permits the partition function and related thermodynamic functions to be evaluated for any temperature and any single site anisotropy from a single data set. Results are presented for the pseudo-critical transition temperature and the maximum in the specific heat as a function of the single site anisotropy parameter. The technique will allow the region near the tricritical point to be explored in detail and will permit the future determination of the zeros of the partition function. It should be noted that the microcanonical sampling method of Lee was found to be unusably slow for the S = 1 problem in regions where the density of states had a significant slope and the microcanonical sampling described in this work is a significant improvement on his sampling method.