Infinite number of exponents for a spin glass transition

Abstract

We consider the behavior of the overlap of $m(\ge 2)$ 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 $\epsilon =d-2$ expansion without using the replica trick.

Revtex, 1 postscript figure available on request (email: [email protected]). To appear in Phys. Rev. B1 Rapid Communication