Branching Transition of a Directed Polymer in Random Medium

TL;DR

This study investigates a phase transition in a 2D directed polymer with branching, revealing a critical point where the polymer shifts from linear to fully branched, characterized by specific scaling exponents.

Contribution

It identifies and characterizes a critical transition in a 2D directed polymer model where branching becomes dominant, providing new scaling exponents at criticality.

Findings

Transition from linear to branched polymer at critical disorder level

Scaling exponents at criticality: ${ar d}_c$, $eta$, and $ u$

Evidence of scale-invariant branching behavior at the transition

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 $\omega_c=0.26 \pm0.02$, in terms of longitudinal distance