The Statistics of Dimers on a Lattice

I. The Number of Dimer Arrangements on a Quadratic Lattice
  • P. W. Kasteleyn
Part of the Modern Birkhäuser Classics book series (MBC)


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.


Partition Function Combinatorial Problem Triangular Array Standard Configuration Quadratic Lattice 
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Copyright information

© Birkhäuser Boston, a part of Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • P. W. Kasteleyn
    • 1
  1. 1.Koninklijke/Shell-LaboratoriumShell Internationale Research Maatschappij N.V.AmsterdamNederland

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