Estimation of the Equilibrium Properties of the Simple AB Alloy

Abstract

Simulation estimates are presented for the equilibrium values of energy, long-range order and particle concentration as functions of temperature and chemical potential for the AB aIloy set on a simple square lattice. The simulation was based on a simple Markov process with transitions defined in terms of particle exchange between nearest-neighbour lattice sites. An ensemble mode of relaxation, employing an ensemble of five 32 x 32-particle samples from the aIloy, was used in order to reduce the level of the fluctuations. The usual periodic boundary conditions were replaced by probability boundary conditions where the states of the external lattice site were estimated using probability distribution functions whose lower moments were equal to the running moments of the sample.