Logarithmic corrections in the free energy of monomer-dimer model on plane lattices with free boundaries

TL;DR

This paper investigates the finite-size corrections to the free energy in monomer-dimer models on lattice strips, revealing a logarithmic correction term whose coefficient depends on the number of monomers and the lattice width parity.

Contribution

It introduces an exact computation method showing how the logarithmic correction coefficient varies with monomer count and lattice width parity, generalizing previous single-monomer results.

Findings

Logarithmic correction term in free energy depends on monomer number and lattice width parity.

Coefficient of the correction equals v for odd n, v/2 for even n.

Results extend previous single-monomer findings to arbitrary monomer counts.

Abstract

Using exact computations we study the classical hard-core monomer-dimer models on m x n plane lattice strips with free boundaries. For an arbitrary number v of monomers (or vacancies), we found a logarithmic correction term in the finite-size correction of the free energy. The coefficient of the logarithmic correction term depends on the number of monomers present (v) and the parity of the width n of the lattice strip: the coefficient equals to v when n is odd, and v/2 when n is even. The results are generalizations of the previous results for a single monomer in an otherwise fully packed lattice of dimers.