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We consider a two-dimensional (d=2) kagom\'e lattice gas model withattractive three-particle interactions around each triangular face of thekagom\'e lattice. Exact solutions are obtained for multiparticle correlationsalong the liquid and vapor branches of the coexistence curve and atcriticality. The correlation solutions are also determined along thecontinuation of the curvilinear diameter of the coexistence region into thedisordered fluid region. The method generates a linear algebraic system ofcorrelation identities with coefficients dependent only upon the interactionparameter. Using a priori knowledge of pertinent solutions for the density andelementary triplet correlation, one finds a closed and linearly independent setof correlation identities defined upon a spatially compact nine-site cluster ofthe kagom\'e lattice. Resulting exact solution curves of the correlations areplotted and discussed as functions of the temperature, and are compared withcorresponding results in a traditional kagom\'e lattice gas havingnearest-neighbor pair interactions. An example of application for themultiparticle correlations is demonstrated in cavitation theory.

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