Phase Transition in a Model with Non-Compact Symmetry on Bethe Lattice   and the Replica Limit
  We solve $O(n,1)$ nonlinear vector model on Bethe lattice and show that it exhibits a transition from ordered to disordered state for $0 \leq n < 1$. If the replica limit $n\to 0$ is taken carefully, the model is shown to reduce to the corresponding supersymmetric model. The latter was introduced by Zirnbauer as a toy model for the Anderson localization transition. We argue thus that the non-compact replica models describe correctly the Anderson transition features. This should be contrasted to their failure in the case of the level correlation problem. 
Ilya A. Gruzberg (Yale University) and Alexander D. Mirlin (University   of Karlsruhe)