A Pfaffian Formula for Monomer–Dimer Partition Functions

@article{Giuliani2015APF,
  title={A Pfaffian Formula for Monomer–Dimer Partition Functions},
  author={Alessandro Giuliani and Ian Jauslin and Elliott H. Lieb},
  journal={Journal of Statistical Physics},
  year={2015},
  volume={163},
  pages={211-238}
}
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… 
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