Solutions for correlations along the coexistence curve and at the critical point of a kagome lattice gas with three-particle interactions

We consider a two-dimensional (d=2) kagome lattice gas model with attractive three-particle interactions around each triangular face of the kagome lattice. Exact solutions are obtained for multiparticle correlations along the liquid and vapor branches of the coexistence curve and at criticality. The correlation solutions are also determined along the continuation of the curvilinear diameter of the coexistence region into the disordered fluid region. The method generates a linear algebraic system of correlation identities with coefficients dependent only upon the interaction parameter. Using a priori knowledge of pertinent solutions for the density and elementary triplet correlation, one finds a closed and linearly independent set of correlation identities defined upon a spatially compact nine-site cluster of the kagome lattice. Resulting exact solution curves of the correlations are plotted and discussed as functions of the temperature, and are compared with corresponding results in a traditional kagome lattice gas having nearest-neighbor pair interactions. An example of application for the multiparticle correlations is demonstrated in cavitation theory.