High-precision percolation thresholds and Potts-model critical manifolds from graph polynomials

@article{Jacobsen2014HighprecisionPT,
  title={High-precision percolation thresholds and Potts-model critical manifolds from graph polynomials},
  author={Jesper Lykke Jacobsen},
  journal={Journal of Physics A: Mathematical and Theoretical},
  year={2014},
  volume={47}
}
  • J. Jacobsen
  • Published 30 January 2014
  • Mathematics
  • Journal of Physics A: Mathematical and Theoretical
The critical curves of the q-state Potts model can be determined exactly for regular two-dimensional lattices G that are of the three-terminal type. This comprises the square, triangular, hexagonal and bow–tie lattices. Jacobsen and Scullard have defined a graph polynomial PB(q, v) that gives access to the critical manifold for general lattices. It depends on a finite repeating part of the lattice, called the basis B, and its real roots in the temperature variable v = eK − 1 provide… 

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