Multi-site correlation functions in two-dimensional lattice gases

The three- and four-site-correlation functions in a two-dimensional Ising-Peierls square lattice gas are computed by means of the cluster variation method (CVM) introduced by Kikuchi. The non-linear CVM equations are numerically solved and the values of several multi-site correlation functions are compared with the results of Monte Carlo simulations at four different coverages (θ = 1/8, 1/4, 1/2, 3/4) as functions of the lateral coupling βj. The results obtained by CVM are accurate within few percent at all coverages and lateral couplings taken into account. Thus the CVM results are used as a basis for a discussion of the validity of the Kirkwood superposition approximation in lattice gases.