Close to Close Packing

Abstract

For various lattice gas models with nearest neighbor exclusion (and, in one case, second-nearest neighbor exclusion as well), we obtain lower bounds on m, the average number of particles on the nonexcluded lattice sites closest to a given particle. They are all of the form m/m _cp ≥1−const·(N _cp /N−1), where N is the number of occupied sites, m _cp is the value of m at close packing, and N _cp is the value of N at close packing. An analogous result exists for hard disks in the plane.