Exact Solution of a Monomer-Dimer Problem: A Single Boundary Monomer on a Non-Bipartite Lattice
Statistical Mechanics
2011-04-13 v2 Combinatorics
Abstract
We solve the monomer-dimer problem on a non-bipartite lattice, the simple quartic lattice with cylindrical boundary conditions, with a single monomer residing on the boundary. Due to the non-bipartite nature of the lattice, the well-known method of a Temperley bijection of solving single-monomer problems cannot be used. In this paper we derive the solution by mapping the problem onto one on close-packed dimers on a related lattice. Finite-size analysis of the solution is carried out. We find from asymptotic expansions of the free energy that the central charge in the logarithmic conformal field theory assumes the value .
Keywords
Cite
@article{arxiv.1010.0050,
title = {Exact Solution of a Monomer-Dimer Problem: A Single Boundary Monomer on a Non-Bipartite Lattice},
author = {F. Y. Wu and Wen-Jer Tzeng and N. Sh. Izmailian},
journal= {arXiv preprint arXiv:1010.0050},
year = {2011}
}
Comments
15 pages, 1 figure, submitted to Phy. Rev. E; v2: revised Acknowledgments