Exact entropy of dimer coverings for a class of lattices in three or more dimensions

Abstract

We construct a class of lattices in three and higher dimensions for which the number of dimer coverings can be determined exactly using elementary arguments. These lattices are a generalization of the two-dimensional kagome lattice, and the method also works for graphs without translational symmetry. The partition function for dimer coverings on these lattices can be determined also for a class of assignments of different activities to different edges.

arXiv comment4 pages, 2 figures; added results on partition function when different edges have different weights; modified abstract; added references

References in corpus (7)

• Quantum dimer model on the kagome lattice: solvable dimer liquid and Ising gauge theory
• Coulomb and Liquid Dimer Models in Three Dimensions
• Dimers on two-dimensional lattices
• Quantum dimer model with extensive ground-state entropy on the kagome lattice
• Quantum dimer models and effective Hamiltonians on the pyrochlore lattice
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Cited by in corpus (6)

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• Entropy of fully packed hard rigid rods on $d$-dimensional hyper-cubic lattices
• Different phases of a system of hard rods on three dimensional cubic lattice
• Exact solution of the $2d$ dimer model: Corner free energy, correlation functions and combinatorics
• Statistics of close-packed dimers on fractal lattices
• Depleted pyrochlore antiferromagnets