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An Asymptotic Expansion and Recursive Inequalities for the Monomer-Dimer Problem

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Title: An Asymptotic Expansion and Recursive Inequalities for the Monomer-Dimer Problem
Author(s): Federbush, Paul; Friedland, Shmuel
Subject(s): monomer-dimer entropies asymptotic expansion recursive inequalities conjecture
Abstract: Let lambda(d)(p) be the p monomer-dimer entropy on the d-dimensional integer lattice Z(d), where p is an element of [0, 1] is the dimer density. We give upper and lower bounds for lambda(d)(p) in terms of expressions involving lambda(d-1)(q). The upper bound is based on a conjecture claiming that the p monomer-dimer entropy of an infinite subset of Z(d) is bounded above by lambda(d)(p). We compute the first three terms in the formal asymptotic expansion of lambda(d)(p) in powers of 1/d. We prove that the lower asymptotic matching conjecture is satisfied for lambda(d)(p). Converted to a power series in p, our " formal" expansion shows remarkable validity in low dimensions, d = 1, 2, 3, in which dimensions we give some numerical studies.
Issue Date: 2011-04
Publisher: Springer Verlag
Citation Info: Federbush, P. & Friedland, S. 2011. An Asymptotic Expansion and Recursive Inequalities for the Monomer-Dimer Problem. Journal of Statistical Physics, 143(2): 306-325. DOI: 10.1007/s10955-011-0170-6
Type: Article
Description: Post print version of article may differ from published version. The original publication is available at www.springerlink.com; DOI: 10.1007/s10955-011-0170-6.
URI: http://hdl.handle.net/10027/7685
ISSN: 0022-4715
Date Available in INDIGO: 2011-05-26
 

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