The diagram approximation for lattice systems

We suggest a new approximation for evaluating the thermodynamical and structural characteristics of lattice gases with attractive nearest neighbor interactions. Mean potentials, which nullify the two-vertex diagram contributions to the free energy diagram expansion, are introduced. The contribution of the lowest-order irreducible diagram with an adjustable parameter is taken into account. This parameter is determined from the requirement that the critical temperature coincides with its exact or best known value. The resulting expressions for the free energy, chemical potential and distribution functions are given in an analytical form. In spite of its simplicity, this approximation yields surprisingly accurate results for different types of two- and three-dimensional lattices. (C) 2001 Elsevier Science B.V. All rights reserved.