PACKING ENTROPY OF EXTENDED, HARD, RIGID OBJECTS ON A LATTICE

We present a systematic method of evaluating the packing entropy for a set of mutually avoiding extended, hard, rigid objects on a lattice. The method generalizes a simple algebraic representation of the lattice cluster theory developed by Freed and co-workers for systems composed of flexible objects. The theory provides a power series expansion in z-1 for the corrections to the zeroth order mean field approximation partition function, where z is the lattice coordination number. We illustrate the general theory by calculating the packing entropy of four-unit rigid ''square'' objects on a hypercubic lattice as a function of the volume fraction of the squares. As a particular limiting case, we also evaluate for the packing entropy of two, three, and four squares on a two-dimensional square lattice and find agreement with the cluster expansion.