Singularities of the renormalization-group flow for random elastic manifolds

We consider the singularities of the zero-temperature renormalization-group how for random elastic manifolds. When starting from small scales, this fl ow goes through two particular points l* and I-c, where the average value o f the random squared potential [U-2] turns negative (l*) and where the four th derivative of the potential correlator becomes infinite at the origin (I -c). The latter point sets the scale where simple perturbation theory break s down as a consequence of the competition between many metastable states. We show that under physically well defined circumstances l(c)<l* and thus t he apparent renormalization of [U*] to negative values does not take place. [S0163-1829(99)06301-8].