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

2004/02/01 by Shmuel Friedland, Friedland, Shmuel, Uri N. Peled +1 · 2 citations
Mathematics · Physics and Astronomy · #05A16 (Secondary) #28D20 #37M25 (Primary) #82B20 #Chemical Physics (physics.chem-ph) #Combinatorics (math.CO) #FOS: Mathematics #FOS: Physical sciences #Markov Chains and Monte Carlo Methods #Mathematical Physics (math-ph) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #math-ph #math.CO #math.MP #msc:05A16 #msc:28D20 #msc:37M25 #msc:82B20 #physics.chem-ph

paper · pdf · doi:10.48550/arxiv.math/0402009

35 pages, one pstricks and two eps figures, submitted

arxiv created 2004/02/01 · openalex publication_date 2004/02/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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%.

Citations

• The undecidability of the domino problem

Cited by

• A new upper bound on the dimer constant of ℤ³
• Independent Set Enumeration and Estimation of Related Constants of Grid Graphs and Their Variants

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