Equation of state of the rigid disk fluid from its triangle distribution

The distribution function f((3)) for triplets of mutual nearest neighbors o ffers a description of local order for many-particle systems confined to a plane. This paper proposes a self-consistent theory for f((3)) in the case of the classical rigid disk model, using three basic identities for closure . Numerical analysis of the resulting coupled nonlinear integral equations yields predictions for the pressure, the boundary tension, and the Kirkwood superposition defect for three disks in mutual contact. The approximation employed implicitly constrains the disk system to remain in the fluid phase at all densities up to close packing (rhoa(2)=2/3(1/2)). The pressure and boundary tension agree reasonably well with the corresponding predictions o f the two-dimensional scaled particle theory, but the former agrees even be tter with a rational approximant due to Sanchez that reproduces eight viria l coefficients. (C) 2000 American Institute of Physics. [S0021-9606(00)5034 6-8].