# 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
}
}
• Published 1 October 2010
• Mathematics
• Physical review. E, Statistical, nonlinear, and soft matter physics
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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