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

Yong Kong
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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.

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Yong Kong. 2006-01-25. Logarithmic corrections in the free energy of monomer-dimer model on plane lattices with free boundaries. https://doi.org/10.1103/physreve.74.011102

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