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arXiv · 1010.0050

Exact Solution of a Monomer-Dimer Problem: A Single Boundary Monomer on a Non-Bipartite Lattice

F. Y. Wu·Wen-Jer Tzeng·N. Sh. Izmailian
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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 $c=-2$.

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F. Y. Wu, Wen-Jer Tzeng, N. Sh. Izmailian. 2010-10-01. Exact Solution of a Monomer-Dimer Problem: A Single Boundary Monomer on a Non-Bipartite Lattice. https://doi.org/10.1103/physreve.83.011106

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