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The Dimer Gas Mayer Series, the Monomer-Dimer lambda_d(p), the Federbush Relation
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The author and Shmuel Friedland recently presented an expression for lambda_d(p) of the monomer-dimer problem involving a power series in p . Herein I present a simple way to derive this expression for lambda_d(p) from the Mayer (or Virial) series of a dimer gas. The derivation is an exercise in basic statistical mechanics. We expect the relationship to be very useful.
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The Aesthetic Asymptotics of the Mayer Series Coefficients for a Dimer Gas on a Regular Lattice
The paper conjectures an asymptotic form for Mayer series coefficients b(n) on regular lattices and reports good numerical agreement when fitting four parameters to the first 20 known coefficients on several bipartite...
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