Lattice statistics using Toeplitz matrices

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Abstract
A new technique is presented for the exact calculation of both low and high density virial coefficients for lattice gases. The virial coefficients are given directly in terms of matrix products using symmetry reduced matrices as elements in a Toeplitz hypermatrix. The technique is applied to the plane−square lattice with nearest neighbor exclusion and next nearest neighbor attraction between particles. Eleven terms are given as explicit functions of the particle interaction energy in both the high and low density virial series; two variants of the basic model are also treated. For the hard core high density series, 14 virial coefficients are calculated exactly.