A Pfaffian formula for monomer-dimer partition functions
Alessandro Giuliani, Ian Jauslin, Elliott H. Lieb
We consider the monomer-dimer partition function on arbitrary finite planar graphs and arbitrary monomer and dimer weights, with the restriction that the only non-zero 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.
- tarball: 15gjl-1.1.tar.gz
- git repository: 15gjl-git (the git repository contains detailed information about the changes in the paper as well as the source code for all previous versions).
- arXiv preprint: arXiv:1510.05027.
- peer-reviewed version, published in the Journal of Statistical Physics, Volume 163, issue 2, page 211-238, doi:10.1007/s10955-016-1484-1
This work has been presented at the following conferences:
[Tr16]: A Pfaffian formula for monomer-dimer partition functions
Geometric and Analytic Theory of Hamiltonian Systems in Finite and Infinite Dimensions, SISSA, Trieste, Italy, Jan 19 2016
[Co16]: A Pfaffian formula for monomer-dimer partition functions
Copenhagen University, Denmark, Jan 13 2016