Entropy of fully packed hard rigid rods on d-dimensional hypercubic lattices

Abstract

We determine the asymptotic behavior of the entropy of full coverings of a L x M square lattice by rods of size k x 1 and 1 x k, in the limit of large k. We show that full coverage is possible only if at least one of L and M is a multiple of k, and that all allowed configurations can be reached from a standard configuration of all rods being parallel, using only basic flip moves that replace a k x k square of parallel horizontal rods by vertical rods, and vice versa. In the limit of large k, we show that the entropy per site S-2 (k) tends to Ak(-2) ln k, with A = 1. We conjecture, based on a perturbative series expansion, that this large-k behavior of entropy per site is superuniversal and continues to hold on all d-dimensional hypercubic lattices, with d >= 2.