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
        }
}
  • F. Y. Wu, W. Tzeng, N. Izmailian
  • Published 1 October 2010
  • Mathematics, Physics, Medicine
  • 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… 
View on PubMed
arxiv.org
8 Citations
Background Citations
3

Figures, Tables, and Topics from this paper

8 Citations

Citation Type

Citation Type

A Pfaffian Formula for Monomer–Dimer Partition Functions
We consider the monomer–dimer partition function on arbitrary finite planar graphs and arbitrary monomer and dimer weights, with the restriction that the only non-zero monomer weights are those on…
A Pfaffian formula for the monomer–dimer model on surface graphs
AbstractWe consider the monomer–dimer model on weighted graphs embedded in surfaces with boundary, with the restriction that only monomers located on the boundary are allowed. We give a Pfaffian…
Exact solution of the 2d dimer model: Corner free energy, correlation functions and combinatorics
Abstract In this work, some classical results of the pfaffian theory of the dimer model based on the work of Kasteleyn, Fisher and Temperley are introduced in a fermionic framework. Then we shall…
Finite size and boundary effects in critical two-dimensional free-fermion models
Abstract Here we will consider the finite-size scaling, finite-size corrections and boundary effects for the critical two-dimensional free-fermion models. A short review of significant achievements…
Specific heat and partition function zeros for the dimer model on the checkerboard B lattice: Finite-size effects.
TLDR
The partition function of the dimer model on a 2M×2N checkerboard B lattice wrapped on a torus is analyzed and very unusual behavior of the partition function zeros and the specific heat of the Dimer model is found.
Finite-size effects for anisotropic 2D Ising model with various boundary conditions
We analyze the exact partition function of the anisotropic Ising model on finite M × N rectangular lattices under four different boundary conditions (periodic–periodic (pp), periodic–antiperiodic…
The dimer and Ising models on non-orientable surfaces
Le but de cette these est d'etudier le modele des dimeres, le modele des monomeres-dimeres, et le modele d'Ising, plus particulierement les fonctions de partition de ces modeles pour des graphes…
Spanning tree generating functions and Mahler measures
We define the notion of a spanning tree generating function (STGF) $\sum a_n z^n$, which gives the spanning tree constant when evaluated at $z=1,$ and gives the lattice Green function (LGF) when…

References

SHOWING 1-10 OF 21 REFERENCES
Table of Integrals, Series, and Products
Introduction. Elementary Functions. Indefinite Integrals of Elementary Functions. Definite Integrals of Elementary Functions. Indefinite Integrals of Special Functions. Definite Integrals of Special…
Phys
  • Rev. E 74, 020104(R)
  • 2006
Phys
  • 110, 671
  • 2003
in Combinatorics: Proceedings of the British Combinatorial Conference
  • London Mathematical Society Lecture Notes Series, Vol. 13
  • 1974
Phil
  • Mag. 6, 1061
  • 1961
Philos
  • Mag. 6, 1061
  • 1961
Phys
  • Rev. 124, 1664
  • 1961
Physica (Amsterdam) 27
  • 1209
  • 1961
Physica 27
  • 1209
  • 1961
Izmailian
  • K. B. Oganesyan, and C.-K. Hu, Phys. Rev. E 67, 066114
  • 2003
...
1
2
3
...