High-order cluster integrals for the lattice-gas model

In the paper, for the known statistical lattice-gas model, a new method is proposed to define the high-order reducible cluster integrals on the basis of the Cauchy--Hadamard theorem and recently established strict information about the convergence radius of the virial expansions for pressure and density in powers of activity. Compared with previous studies (where the whole set of reducible cluster integrals were evaluated on the basis of the extremely limited number of low-order irreducible integrals), the proposed complex method to approximate the reducible cluster integrals yields the theoretical values of pressure at the saturation and boiling points considerably close to each other as well as to the Lee--Yang solution for the two-dimensional lattice gas.