By using the asymptotic theory of Pemantle and Wilson, exact asymptotic
expansions of the free energy of the monomer-dimer model on rectangular nΓβ 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 nΓβ
lattice strip has exactly the same first n terms in the series expansion as
that of infinite βΓβ lattice.Comment: 9 pages, 6 table