2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/27462We consider the behavior of the overlap of $m (\geq 2)$ paths at the spin glass transition for a directed polymer in a random medium. We show that an infinite number of exponents is required to describe these overlaps. This is done in an $ε= d-2$ expansion without using the replica trick.Revtex, 1 postscript figure available on request (email: sb@iopb.ernet.in). To appear in Phys. Rev. B1 Rapid CommunicationCondensed Mattertext