High-temperature expansion for Ising models on quasiperiodic tilings

@article{Repetowicz1999HightemperatureEF,
  title={High-temperature expansion for Ising models on quasiperiodic tilings},
  author={Przemysław Repetowicz and Uwe Grimm and Michael Schreiber},
  journal={Journal of Physics A},
  year={1999},
  volume={32},
  pages={4397-4418}
}
We consider high-temperature expansions for the free energy of zero-field Ising models on planar quasiperiodic graphs. For the Penrose and the octagonal Ammann-Beenker tiling, we compute the expansion coefficients up to 18th order. As a by-product, we obtain exact vertex-averaged numbers of self-avoiding polygons on these quasiperiodic graphs. In addition, we analyse periodic approximants by computing the partition function via the Kac-Ward determinant. It turns out that the series expansions… 
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