Approximation of Cluster Integrals for Various Lattice-Gas Models

An approximation for cluster integrals of an arbitrary high order has been proposed for the well-known lattice-gas model with an arbitrary geometry and dimensions. The approximation is based on the recently obtained accurate relations for the convergence radius of the virial power series in the activity parameter for the pressure and density. As compared to the previous studies of the symmetric virial expansions for the gaseous and condensed states of a lattice gas, the proposed approximation substantially approaches the pressure values at the saturation and boiling points. For the Lee–Yang lattice-gas model, the approximation considerably improves the convergence to the known exact solution.