Branching Transition of a Directed Polymer in Random Medium

Abstract

A directed polymer is allowed to branch, with configurations determined by global energy optimization and disorder. A finite size scaling analysis in 2D shows that, if disorder makes branching more and more favorable, a critical transition occurs from the linear scaling regime first studied by Huse and Henley [Phys. Rev. Lett. 54, 2708 (1985)] to a fully branched, compact one. At criticality clear evidence is obtained that the polymer branches at all scales with dimension ${\bar{d}}_c$ and roughness exponent ${\zeta }_c$ satisfying $({\bar{d}}_c-1)/{\zeta }_c=0.13\pm 0.01$, and energy fluctuation exponent ${\omega }_c=0.26\pm 0.02$, in terms of longitudinal distance

REVTEX, 4 pages, 3 encapsulated eps figures