The monomer-dimer model is fundamental in statistical mechanics. However, it
is #P-complete in computation, even for two dimensional problems. A
formulation in matrix permanent for the partition function of the monomer-dimer
model is proposed in this paper, by transforming the number of all matchings of
a bipartite graph into the number of perfect matchings of an extended bipartite
graph, which can be given by a matrix permanent. Sequential importance sampling
algorithm is applied to compute the permanents. For two-dimensional lattice
with periodic condition, we obtain 0.6627±0.0002, where the exact value is
h2​=0.662798972834. For three-dimensional lattice with periodic condition,
our numerical result is 0.7847±0.0014, {which agrees with the best known
bound 0.7653≤h3​≤0.7862.}Comment: 6 pages, 2 figure