The statistics of dimers on a lattice : I. The number of dimer arrangements on a quadratic lattice
Abstract
The number of ways in which a finite quadratic lattice (with edges or with periodic boundary conditions) can be fully covered with given numbers of “horizontal” and “vertical” dimers is rigorously calculated by a combinatorial method involving Pfaffians. For lattices infinite in one or two dimensions asymptotic expressions for this number of dimer configurations are derived, and as an application the entropy of a mixture of dimers of two different lengths on an infinite rectangular lattice is calculated. The relation of this combinatorial problem to the Ising problem is briefly discussed.
- Publication:
-
Physica
- Pub Date:
- December 1961
- DOI:
- 10.1016/0031-8914(61)90063-5
- Bibcode:
- 1961Phy....27.1209K