Pair-correlation function in 2-dimensional lattice gases

Abstract

The pair-correlation function in two-dimensional lattice gases is computed by means of three discretized classical equations for the structure of liquids: the hypernetted-chain, the Percus-Yevick, and the crossover integral equations. The equations are numerically solved by an iteration procedure. Two different systems are considered: the Ising-Peierls lattice gas with nearest-neighbor interactions and a model for O adsorbed on the W(110) surface, in which interactions up to the fourth neighbors are taken into account. The values of the pair-correlation function for nearest, next-nearest, and next-next-nearest neighbors are compared with the results of Monte Carlo simulations at four different coverages Θ (Θ=1/8, 1) / 4 ,1/2,3/4) as functions of the lateral coupling. It turns out that the crossover integral equation gives the best agreement with Monte Carlo data in both systems, being accurate especially at low Θ, whereas the Percus-Yevick equation fails in a wide range of parameters