Singularities of the renormalization group flow for random elastic manifolds

Abstract

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.