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 lc, where the average value of the random squared potential U2 turns negative (l*) and where the fourth derivative of the potential correlator becomes infinite at the origin (lc). 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 lc<l* and thus the apparent renormalization of U2 to negative values does not take place.
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