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

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.

4 pages, 2 figures

References in corpus (3)

• Interacting classical dimers on the square lattice
• Logarithmic Conformal Field Theory and Boundary Effects in the Dimer Model
• Packing dimers on $(2p+1)\times (2q+1)$ lattices

Cited by in corpus (13)

• Recursion-transform method on computing the complex resistor network with three arbitrary boundaries
• Monomer-dimer model in two-dimensional rectangular lattices with fixed dimer density
• Dimer-monomer model on the Sierpinski gasket
• The Pfaffian solution of a dimer-monomer problem: Single monomer on the boundary
• Exact solution of the $2d$ dimer model: Corner free energy, correlation functions and combinatorics
• The dimer model on the triangular lattice
• Boundary monomers in the dimer model
• Non-Local Finite-Size Effects in the Dimer Model
• Exact asymptotics of monomer-dimer model on rectangular semi-infinite lattices
• Finite-size corrections and scaling for the dimer model on the checkerboard lattice
• A Statistical Model of Current Loops and Magnetic Monopoles
• Asymptotic behavior of the entropy of chains placed on stripes
• Recurrence solution of monomer-polymer models on two-dimensional rectangular lattices