Dimer Statistics on a Bethe Lattice

Loading...
Thumbnail Image
Penn collection
Department of Physics Papers
Degree type
Discipline
Subject
Physical Sciences and Mathematics
Physics
Funder
Grant number
License
Copyright date
Distributor
Related resources
Author
Cohen, Michael
Contributor
Abstract

We discuss the exact solutions of various models of the statistics of dimer coverings of a Bethe lattice.We reproduce the well-known exact result for noninteracting hard-core dimers by both a very simple geometrical argument and a general algebraic formulation for lattice statistical problems. The algebraic formulation enables us to discuss loop corrections for finite dimensional lattices. For the Bethe lattice we also obtain the exact solution when either (a) the dimers interact via a short-range interaction or (b) the underlying lattice is anisotropic. We give the exact solution for a special limit of dimers on a Bethe lattice in a quenched random potential in which we consider the maximal covering of dimers on random clusters at site occupation probability p. Surprisingly the partition function for “maximal coverage” on the Bethe lattice is identical to that for the statistics of branched polymers when the activity for a monomer unit is set equal to −p. Finally we give an exact solution for the number of residual vacancies when hard-core dimers are randomly deposited on a one dimensional lattice.

Advisor
Date Range for Data Collection (Start Date)
Date Range for Data Collection (End Date)
Digital Object Identifier
Series name and number
Publication date
2006-11-13
Journal title
Volume number
Issue number
Publisher
Publisher DOI
Journal Issue
Comments
Suggested Citation: Harris, A.B. and Cohen, M. (2006). Dimer statistics on a Bethe lattice. The Journal of Chemical Physics 125, 184107. © 2006 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in The Journal of Chemical Physics and may be found at http://dx.doi.org/10.1063/1.2364501.
Recommended citation
Collection