On the Validations of the Asymptotic Matching Conjectures

@article{Friedland2006OnTV,
  title={On the Validations of the Asymptotic Matching Conjectures},
  author={S. Friedland and E. Krop and P. H. Lundow and K. Markstr{\"o}m},
  journal={Journal of Statistical Physics},
  year={2006},
  volume={133},
  pages={513-533}
}
  • S. Friedland, E. Krop, +1 author K. Markström
  • Published 2006
  • Mathematics, Physics
  • Journal of Statistical Physics
  • 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… CONTINUE READING
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