Abstract
The authors describe the construction of regular lattices in two-dimensional hyperbolic space by means of the action of a discrete subgroups of SU(1,1). They consider an Ising model on such lattices and show how the thermodynamic limit can be handled. They give high- and low-temperature expansions of the free energy, magnetic susceptibility and magnetization and find that these quantities diverge at a critical temperature with mean-field exponents beta =1/2, gamma =1. They also conjecture the long distance behaviour of correlation functions at the critical temperature.