Renormalization group approach to three-state spin models in two dimensions

The real space renormalization group approach is used to study spin one anisotropic models with dipolar and quadrupolar interactions on the triangular lattice. The method is tested for the three state Potts model and the Blume-Emery-Griffiths model leading to results which are basically in agreement with other treatments of these models. The phase diagram for a quadrupolar model (anisotropic Potts model) is obtained and the influence of an external magnetic field on the transition temperature to the quadrupolar phase is determined. The fixed point which controls a transition to the phase with Ising dipolar order andXY-type quadrupolar order is found.Work performed within the research program of the Sonderforschungsbereich 341, Köln-Aachen-Jülich