On the Validations of the Asymptotic Matching Conjectures
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- Friedland, S., Krop, E., Lundow, P.H. et al. J Stat Phys (2008) 133: 513. doi:10.1007/s10955-008-9550-y
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In this paper we review the asymptotic matching conjectures for r-regular bipartite graphs, and their connections in estimating the monomer-dimer entropies in d-dimensional integer lattice and Bethe lattices. We prove new rigorous upper and lower bounds for the monomer-dimer entropies, which support these conjectures. We describe a general construction of infinite families of r-regular tori graphs and give algorithms for computing the monomer-dimer entropy of density p, for any p∈[0,1], for these graphs. Finally we use tori graphs to test the asymptotic matching conjectures for certain infinite r-regular bipartite graphs.
KeywordsMatching and asymptotic growth of average matchings for r-regular bipartite graphs Monomer-dimer partitions and entropies
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