Lattice hard spheres

Lattice hard spheres refers to athermal lattice gas models, in which pairs of sites separated by less than some short distance $\sigma$ cannot be simultaneously occupied.

Basically the differences with the standard lattice gas model (Ising model) are:

• An occupied site excludes the occupation of some of the neighboring sites.

• No energy interactions between pairs of occupied sites are considered.

These systems exhibit phase (order-disorder) transitions

• See Ref. 1 for some results of three-dimensional lattice hard sphere systems (on a simple cubic lattice)

• See Ref 2. for results of two-dimensional systems (lattice hard disks) on a square lattice.

References

1. A. Z. Panagiotopoulos, "Thermodynamic properties of lattice hard-sphere models", J. Chem. Phys. 123, 104504 (2005)
2. Heitor C. Marques Fernandes, Jeferson J. Arenzon, and Yan Levin "Monte Carlo simulations of two-dimensional hard core lattice gases" J. Chem. Phys. 126, 114508 (2007).