Fluctuation exponents for directed polymers in the intermediate disorder regime

TL;DR

This paper calculates fluctuation exponents for a solvable 1D directed polymer model in the intermediate disorder regime, aligning with KPZ predictions and connecting to the KPZ equation's solutions.

Contribution

It provides explicit fluctuation exponents in the intermediate disorder regime, confirming KPZ scaling and linking to the Cole-Hopf KPZ equation solutions.

Findings

Exponents satisfy KPZ scaling relation.

Exponents match physical predictions.

Recovers KPZ exponents in critical case.

Abstract

We compute the fluctuation exponents for a solvable model of one-dimensional directed polymers in random environment in the intermediate regime. This regime corresponds to taking the inverse temperature to zero with the size of the system. The exponents satisfy the KPZ scaling relation and coincide with physical predictions. In the critical case, we recover the fluctuation exponents of the Cole-Hopf solution of the KPZ equation in equilibrium and close to equilibrium.