Exact solution of a monomerdimer problem: A single boundary monomer on a nonbipartite lattice
Abstract
We solve the monomerdimer 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 wellknown method of solving singlemonomer problems with a Temperley bijection cannot be used. In this paper, we derive the solution by mapping the problem onto one of closedpacked dimers on a related lattice. Finitesize 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.
 Publication:

Physical Review E
 Pub Date:
 January 2011
 DOI:
 10.1103/PhysRevE.83.011106
 arXiv:
 arXiv:1010.0050
 Bibcode:
 2011PhRvE..83a1106W
 Keywords:

 05.50.+q;
 02.10.Ox;
 11.25.Hf;
 Lattice theory and statistics;
 Combinatorics;
 graph theory;
 Conformal field theory algebraic structures;
 Condensed Matter  Statistical Mechanics;
 Mathematics  Combinatorics
 EPrint:
 15 pages, 1 figure, submitted to Phy. Rev. E