Theory of Computation of Multidimensional Entropy with an Application to the Monomer-Dimer Problem

Details Theory of Computation of Multidimensional Entropy with an Application to the Monomer-Dimer Problem Theory of Computation of Multidimensional Entropy with an Application to the Monomer-Dimer Problem

2004-02-01

arxiv.org/abs/math/0402009v1

Mathematics

Combinatorics

35 pages, one pstricks and two eps figures, submitted

Scientific paper

We outline the most recent theory for the computation of the exponential
growth rate of the number of configurations on a multi-dimensional grid. As an
application we compute the monomer-dimer constant for the 2-dimensional grid to
8 decimal digits, agreeing with the heuristic computations of Baxter, and for
the 3-dimensional grid with an error smaller than 1.35%.

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