Journal of Statistical Physics

, Volume 85, Issue 1–2, pp 251–259 | Cite as

Ising models on hyperbolic graphs

  • C. Chris Wu
Short Communications


We consider Ising models on a hyperbolic graph which, loosely speaking, is a discretization of the hyperbolic planeH2 in the same sense asZ d is a discretization ofR d . We prove that the models exhibit multiple phase transitions. Analogous results for Potts models can be obtained in the same way.

Key Words

Ising/Potts models Fortuin-Kasteleyn random cluster models hyperbolic graphs 


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Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • C. Chris Wu
    • 1
  1. 1.Department of MathematicsPennsylvania State UniversityMonaca

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