Theory of computation of multidimensional entropy with an application to the monomer–dimer problem

Consider all colorings of a finite box in a multidimensional grid with a given number of colors subject to given local constraints. We outline the most recent theory for the computation of the exponential growth rate of the number of such colorings as a function of the dimensions of the box. As an a...

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Published inAdvances in applied mathematics Vol. 34; no. 3; pp. 486 - 522
Main Authors Friedland, Shmuel, Peled, Uri N.
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.04.2005
Subjects
Monomer-dimer
Subshifts of finite type
Topological entropy
Transfer matrix
Transfer matrix
Subshifts of finite type
Topological entropy
Monomer-dimer
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Summary:Consider all colorings of a finite box in a multidimensional grid with a given number of colors subject to given local constraints. We outline the most recent theory for the computation of the exponential growth rate of the number of such colorings as a function of the dimensions of the box. As an application we compute the monomer–dimer constant for the 2-dimensional grid to 9 decimal digits, agreeing with the heuristic computations of Baxter, and for the 3-dimensional grid with an error smaller than 1.35%.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0196-8858
1090-2074
DOI:10.1016/j.aam.2004.08.005