We consider the singularities of the zero temperature renormalization group flow for random elastic manifolds. When starting from small scales, this flow goes through two particular points $l^{ *}$ and $l_{ c}$, where the average value of the random squared potential $<U^{ 2}>$ turnes negative ($l^{ *}$) and where the fourth derivative of the potential correlator becomes infinite at the origin ($l_{ c}$). The latter point sets the scale where simple perturbation theory breaks down as a consequence of the competition between many metastable states. We show that under physically well defined circumstances $l_{ c}<l^{ *}$ and thus the apparent renormalization of $<U^{ 2}>$ to negative values does not take place.
Categories: cond-mat.stat-mech cond-mat.dis-nn cond-mat.supr-con