Microcanonical ensemble Monte Carlo method for discrete systems.

Abstract

In an earlier work [Phys. Rev. A 44, 4061 (1991)] a method of carrying out Monte Carlo simulations in the microcanonical ensemble was discussed and applied to systems described by continuous potentials. This method can also be used for discrete systems, e.g., spin, lattice gas, or alloy type models where it furnishes a different way of exploring the system than the canonical ensemble. A complete statistical mechanics and related thermodynamics exists for this microcanonical ensemble. We give microcanonical ensemble fluctuation formulas for the specific heat and constant energy susceptibility and relate these to the analogous canonical ensemble expressions for the Ising model. As an example we present simulation results for a two-dimensional Ising model and compare the microcanonical and canonical ensemble calculation of various physical properties of the system. An interesting feature is the appearance of a large (16%) ensemble difference between the specific heat in canonical and microcanonical ensemble simulations for a 30\ifmmode\times\else\texttimes\fi{}30 Ising system in the vicinity of the maximum in the specific heat.