The Pfaffian Sign Theorem for the Dimer Model on a Triangular Lattice

@article{Bleher2017ThePS,
  title={The Pfaffian Sign Theorem for the Dimer Model on a Triangular Lattice},
  author={Pavel Bleher and Brad Elwood and Dra{\vz}en Petrovi{\'c}},
  journal={Journal of Statistical Physics},
  year={2017},
  volume={171},
  pages={400-426}
}
We prove the Pfaffian Sign Theorem for the dimer model on a triangular lattice embedded in the torus. More specifically, we prove that the Pfaffian of the Kasteleyn periodic-periodic matrix is negative, while the Pfaffians of the Kasteleyn periodic-antiperiodic, antiperiodic-periodic, and antiperiodic-antiperiodic matrices are all positive. The proof is based on the Kasteleyn identities and on small weight expansions. As an application, we obtain an asymptotic behavior of the dimer model… 
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