Physica 128A (1984) 334-350 North-Holland, Amsterdam GENERALIZED CLUSTER DESCRIPTION OF MULTICOMPONENT SYSTEMS J.M. SANCHEZ Henry Krumb School of Mines, Columbia University, New York, NY 10027, USA F. DUCASTELLE ONERA, 9.320~Chatillon, France D. GRATIAS CECMICNRS, 15, rue Georges Urbain, 944WVitry, France Received 19 January 1984 A general formalism for the description of configurational cluster functions in multicomponent systems is developed. The approach is based on the description of configurational cluster functions in terms of an orthogonal basis in the multidimensional space of discrete spin variables. The formalism is used to characterize the reduced density matrices (or cluster probability densities) and the free energy functional obtained in the Cluster Variation Method approximation. For the parti- cular representation chosen, the expectation values of the base functions are the commonly used multisite correlation functions. The latter form an independent set of variational parameters for the free energy which, in general, facilitates the minimization procedure. A new interpretation of the Cluster Variation Method as a self-consistency relation on the renormalized cluster energies is also presented. 1. Introduction The Cluster Variation Method (CVM) was originally proposed by Kikuchi’) as an approximate technique for the treatment of cooperative phenomena in periodic systems. The method is a non-trivia1 generalization of the mean-field approximation that, although behaving classically near critical points, gives very accurate results outside critical regions. Thus, the CVM is best suited either to study first-order transitions or to investigate the critical behavior of complex systems for which renormalization group techniques cannot be readily implemented. Since Kikuchi’s 1951 paper, the CVM has been reformulated by several authors and applied to a number of two- and three-dimensional Ising lattices with pairs and/or many-body interactions %15).The different formulations of the CVM were motivated by the fact that Kikuchi’s derivation used a com- 0378-4371/84/03.00 @ Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)