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

  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},
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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  • N. IzmailianR. Kenna
  • Physics
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2011
It is found that the dimer model on an M×N triangular lattice wrapped on a torus can be described by a conformal field theory having a central charge c=-2 and the shift exponent for the specific heat is found to depend on the parity of the number of lattice sites N along a given lattice axis.

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  • G. Tesler
  • Mathematics
    J. Comb. Theory, Ser. B
  • 2000
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