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

TL;DR

This paper provides exact solutions for multiparticle correlations in a kagomé lattice gas with three-particle interactions, revealing detailed behavior along the coexistence curve and at criticality, with applications in cavitation theory.

Contribution

It introduces a novel exact solution method for multiparticle correlations in a kagomé lattice gas with three-particle interactions, extending understanding beyond pair interactions.

Findings

Exact correlation solutions along coexistence and critical points

Correlation behavior compared with nearest-neighbor pair interaction models

Application of correlations in cavitation theory

Abstract

We consider a two-dimensional (d=2) kagom\'e lattice gas model with attractive three-particle interactions around each triangular face of the kagom\'e 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 kagom\'e 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 kagom\'e lattice gas having nearest-neighbor pair interactions. An example of application for the multiparticle correlations is demonstrated in cavitation theory.