The Global Phase Diagram of a Modular Invariant Two-dimensional Statistical Model

A generalization of the Coulomb gas model with modular SL(2,Z)-symmetry allows for a discrete infinity of phases which are characterized by the condensation of dyonic pseudoparticles and the breaking of parity and time reversal. Here we study the phase diagram of such a model by using renormalization group techniques. Then the symmetry SL(2,Z) acting on the two-dimensional parameter space gives us a nested shape of its global phase diagram and all the infrared stable fixed points. Finally we propose a connection with the 2-dimensional conformal field theory description of the fractional quantum Hall effect.