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:
 10.1016/00318914(61)900635
 Bibcode:
 1961Phy....27.1209K