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Branching Transition of a Directed Polymer in Random Medium

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 $ζ_c$ satisfying $({\bar d}_c-1)/ζ_c = 0.13\pm 0.01$, and energy fluctuation exponent $ω_c=0.26 \pm0.02$, in terms of longitudinal distance