 
Summary: Equation of state for hardsquare lattice gases
Heitor C. Marques Fernandes,* Yan Levin,
and Jeferson J. Arenzon
Instituto de Física, Universidade Federal do Rio Grande do Sul, Caixa Postale 15051, 91501970 Porto Alegre RS, Brazil
Received 20 November 2006; revised manuscript received 23 February 2007; published 18 May 2007
A simple equation of state is derived for a hardcore lattice gas of side length , and compared to the results
of Monte Carlo simulations. In the disordered fluid phase, the equation is found to work very well for a
twodimensional lattice gas of hard squares and reasonably well for the threedimensional gas of hard cubes.
DOI: 10.1103/PhysRevE.75.052101 PACS number s : 05.50. q
Almost forty years ago, Carnahan and Starling published
their now famous equation of state for a hardsphere fluid
1 . Their derivation was based on the simple observation
that the leading order virial coefficients for a hardsphere
fluid in three dimensions closely followed a geometric se
quence. The assumption that this behavior also extrapolated
to higherorder virials allowed Carnahan and Starling to ex
plicitly resum the virial expansion to find a simple, yet very
accurate, equation of state.
Unfortunately, no such accurate equation of state is
known for the case of lattice gases. This is particularly frus
