HYPERVOLUMES IN MICROCANONICAL MONTE-CARLO

A Monte Carlo method to perform microcanonical simulations by sampling the configurational and momenta spaces is presented. The technique wa s inspired by the method of hypervolumes for calculating the entropy i n a microcanonical ensemble. Although this method is strictly proven i n the thermodynamic limit, the hypervolume Monte Carlo (HVMC) algorith m, presented in this article, works well with a relatively small numbe r of particles. In contrast to other algorithms for microcanonical Mon te Carlo simulations, the HVMC method does not involve previous integr ations over the momenta space or demons. Therefore, it can be used wit h any form of Hamiltonian. Thermal and structural properties for the L ennard-Jones system obtained by NVE molecular dynamics are compared wi th results from the HVMC method. The agreement is excellent. Additiona lly, the method provides the speed distribution functions of the syste m which are, also, in excellent agreement with the results from molecu lar dynamics. A discussion of the HVMC method in the context of the st atistical mechanical theory of the microcanonical ensemble is presente d.