Monomer-dimer model in two-dimensional rectangular lattices with fixed dimer density

Abstract

The classical monomer-dimer model in two-dimensional lattices has been shown to belong to the " #P -complete" class, which indicates the problem is computationally "intractable." We use exact computational method to investigate the number of ways to arrange dimers on m×n two-dimensional rectangular lattice strips with fixed dimer density ρ. For any dimer density 0