PHASE-TRANSITION IN A MODEL WITH NONCOMPACT SYMMETRY ON BETHE LATTICEAND THE REPLICA LIMIT

We solve the O(n, 1) nonlinear vector model on the Bethe lattice and s how that it exhibits a transition from ordered to disordered state for 0 less than or equal to n < 1. If the replica limit n --> 0 is taken carefully, the model is shown to reduce to the corresponding supersymm etric model. The latter was introduced by Zirnbauer as a toy model for the Anderson localization transition. We argue thus that the non-comp act replica models describe correctly the Anderson transition features . This should be contrasted to their failure in the case of the level correlation problem.