# Exact solution of a monomer-dimer problem: a single boundary monomer on a nonbipartite lattice.

@article{Wu2011ExactSO, title={Exact solution of a monomer-dimer problem: a single boundary monomer on a nonbipartite lattice.}, author={F. Y. Wu and W.-J. Tzeng and Nickolay Sh. Izmailian}, journal={Physical review. E, Statistical, nonlinear, and soft matter physics}, year={2011}, volume={83 1 Pt 1}, pages={ 011106 } }

We solve the monomer-dimer problem on a nonbipartite lattice, a simple quartic lattice with cylindrical boundary conditions, with a single monomer residing on the boundary. Due to the nonbipartite nature of the lattice, the well-known method of solving single-monomer problems with a Temperley bijection cannot be used. In this paper, we derive the solution by mapping the problem onto one of closed-packed dimers on a related lattice. Finite-size analysis of the solution is carried out. We find…

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