A Pfaffian formula for monomerdimer partition functions
Alessandro Giuliani, Ian Jauslin, Elliott H. Lieb
2015
Abstract
We consider the monomerdimer partition function on arbitrary finite planar graphs and arbitrary monomer and dimer weights, with the restriction that the only nonzero monomer weights are those on the boundary. We prove a Pfaffian formula for the corresponding partition function. As a consequence of this result, multipoint boundary monomer correlation functions at close packing are shown to satisfy fermionic statistics. Our proof is based on the celebrated Kasteleyn theorem, combined with a theorem on Pfaffians proved by one of the authors, and a careful labeling and directing procedure of the vertices and edges of the graph.
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 arXiv preprint: arXiv:1510.05027.
 peerreviewed version, published in the Journal of Statistical Physics, Volume 163, issue 2, page 211238, doi:10.1007/s1095501614841
Talks
This work has been presented at the following conferences:

[Tr16]: A Pfaffian formula for monomerdimer partition functions
Geometric and Analytic Theory of Hamiltonian Systems in Finite and Infinite Dimensions, SISSA, Trieste, Italy, Jan 19 2016
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[Co16]: A Pfaffian formula for monomerdimer partition functions
University of Copenhagen, Denmark, Jan 13 2016
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