High-activity perturbation expansion for the hard square lattice gas

High-activity perturbation expansion for the hard square lattice gas.

We study a system of particles with nearest- and next-nearest-neighbor exclusion on the square lattice (hard squares). This system undergoes a transition from a fluid phase at low density to a columnar-ordered phase at high density. We develop a systematic high-activity perturbation expansion for the free energy per site about a state with perfect columnar order. We show that the different term...

Finite-size analysis of the hard-square lattice gas.

We investigate the hard-square lattice-gas model by means of transfer-matrix calculations and a finite-size-scaling analysis. Using a minimal set of assumptions we find that the spectrum of correction-to-scaling exponents is consistent with that of the exactly solved Ising model, and that the critical exponents and correlation-length amplitudes closely follow the relation predicted by conformal...

Transfer-Matrix Study of Hard-Core Singularity for Hard-Square Lattice Gas

A singularity on the negative fugacity axis of the hard-square lattice gas is investigated in terms of numerical diagonalization of transfer matrices. The location of the singular point z− c and the critical exponent ν are accurately determined by the phenomenological renormalization technique as −0.11933888188(1) and 0.416667(1), respectively. It is also found that the central charge c and the...

A new statistical mechanical approximation method applied to the two dimensional hard square lattice gas

Equation of state for hard-square lattice gases.

A simple equation of state is derived for a hard-core lattice gas of side length lambda , and compared to the results of Monte Carlo simulations. In the disordered fluid phase, the equation is found to work very well for a two-dimensional lattice gas of hard squares and reasonably well for the three-dimensional gas of hard cubes.