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, (1985) 2708) to a fully branched, compact one. At criticality clear evidence is obtained that the polymer branches at all scales with dimension (d) over bar(c) and roughness exponent zeta(c) satisfying ((d) over bar(c) - 1)/zeta(c) = 0.13 +/- 0.01, and energy fluctuation exponent omega(c) = 0.26 +/- 0.02, in terms of longitudinal distance.