Exact asymptotics of monomer-dimer model on rectangular semi-infinite lattices

Abstract

By using the asymptotic theory of Pemantle and Wilson, exact asymptotic expansions of the free energy of the monomer-dimer model on rectangular $n\times \infty$ lattices in terms of dimer density are obtained for small values of $n$, at both high and low dimer density limits. In the high dimer density limit, the theoretical results confirm the dependence of the free energy on the parity of $n$, a result obtained previously by computational methods. In the low dimer density limit, the free energy on a cylinder $n\times \infty$ lattice strip has exactly the same first $n$ terms in the series expansion as that of infinite $\infty \times \infty$ lattice.

9 pages, 6 tables

References in corpus (4)

• Logarithmic Conformal Field Theory and Boundary Effects in the Dimer Model
• Packing dimers on $(2p+1)\times (2q+1)$ lattices
• Monomer-dimer model in two-dimensional rectangular lattices with fixed dimer density
• Logarithmic corrections in the free energy of monomer-dimer model on plane lattices with free boundaries

Cited by in corpus (4)

• Sequential cavity method for computing free energy and surface pressure
• Asymptotic behavior of the entropy of chains placed on stripes
• Power series expansions for the planar monomer-dimer problem
• Recurrence solution of monomer-polymer models on two-dimensional rectangular lattices