A Pfaffian formula for the monomer–dimer model on surface graphs

@article{Pham2017APF,
  title={A Pfaffian formula for the monomer–dimer model on surface graphs},
  author={Anh Minh Pham},
  journal={Letters in Mathematical Physics},
  year={2017},
  volume={108},
  pages={1885-1904}
}
  • A. Pham
  • Published 2 May 2017
  • Mathematics
  • Letters in Mathematical Physics
AbstractWe consider the monomer–dimer model on weighted graphs embedded in surfaces with boundary, with the restriction that only monomers located on the boundary are allowed. We give a Pfaffian formula for the corresponding partition function, which generalises the one obtained by Giuliani et al. (J Stat Phys 163(2):211–238, 2016) for graphs embedded in the disc. Our proof is based on an extension of a bijective method mentioned in Giuliani et al. (2016), together with the Pfaffian formula… 
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The dimer and Ising models on non-orientable surfaces
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