Dimer Statistics on a Bethe Lattice

Details Dimer Statistics on a Bethe Lattice Dimer Statistics on a Bethe Lattice

2004-08-27

arxiv.org/abs/cond-mat/0408618v1

Physics

Condensed Matter

Statistical Mechanics

20 pages, 8 figures, 34 references

Scientific paper

We discuss the exact solutions of various models of the statistics of dimer coverings of a Bethe lattice. We reproduce the well-known exact results for noninteracting hard-core dimers by both a very simple geometrical argument and a general algebraic formulation for lattice statistical problems. 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 also give solutions for special cases of random lattices and for the jamming limit of one dimensional deposition of dimers.

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