Journal of Statistical Physics, Vol. 85, Nos. 1/2, 1996. p. 251-259.
We consider Ising models on a hyperbolic graph which, loosely speaking, is a discretization of the hyperbolic plane H^2 in tile same sense as Z^d is a discretization of R^d. We prove that the models exhibit multiple phase transitions. Analogous results for Potts models can be obtained in the same way.