Equations of state for classical hard-core systems.

Abstract

A method, based on the first few virial coefficients, is used to generate the pressure P of a classical d-dimensional hard-core system at arbitrary density \ensuremath{\rho}---the method is exact for d=1. The equation of state reproduces all the virial coefficients used on expanding P/${k}_{B}$T about \ensuremath{\rho}=0. Also, P/${\ensuremath{\rho}}_{c}$${k}_{B}$T\ensuremath{\rightarrow}R/(1-\ensuremath{\rho}/${\ensuremath{\rho}}_{c}$) as \ensuremath{\rho}\ensuremath{\rightarrow}${\ensuremath{\rho}}_{c}$ and \ensuremath{\partial}(P/${k}_{B}$T)/\ensuremath{\partial}\ensuremath{\rho}>0 for 0${\ensuremath{\rho}}_{c}$. As the order of the approximation increases, the position ${\ensuremath{\rho}}_{c}$ of the simple pole approaches the density ${\ensuremath{\rho}}_{0}$ of closest packing and the residue R increases beyond the value of the spatial dimensionality d of the system. The equation of state is in rather good agreement with the molecular-dynamics results especially for the case of hard disks as expected.