Ising low-temperature polynomials and hard-sphere gases on cubic lattices of general dimension

TL;DR

This paper derives low-activity and low-density expansions for hard-sphere gases on cubic lattices of any dimension, extending previous Ising model analyses to provide new insights into lattice gas behavior.

Contribution

It introduces a generalized method to compute low-temperature and low-density expansions for hard-sphere gases on cubic lattices of arbitrary dimension, extending prior Ising model techniques.

Findings

13th order expansions derived for various dimensions

Parameter estimates provided for different lattice types

Extension of Ising model low-temperature expansions to lattice gases

Abstract

We derive and analyze the low-activity and low-density expansions of the pressure for the model of a hard-sphere gas on cubic lattices of general dimension $d$, through the 13th order. These calculations are based on our recent extension to dimension d of the low-temperature expansions for the specific free-energy of the spin-1/2 Ising models subject to a uniform magnetic field on the (hyper-)simple-cubic lattices. Estimates of the model parameters are given also for some other lattices