Scaling properties of (2+1) directed polymers in the low temperature limit

TL;DR

This paper uses the replica method to analyze the low temperature behavior of (2+1) directed polymers in a random potential, estimating the free energy fluctuation exponent and its distribution tail.

Contribution

It introduces a novel approach to compute the free energy fluctuation exponent and the distribution tail for (2+1) directed polymers at low temperature.

Findings

Estimated the fluctuation exponent as 1/4

Derived the left tail of the free energy distribution

Compared the theoretical exponent with numerical results

Abstract

In terms of the replica method we consider the low temperature limit of (2+1) directed polymers in a random potential. The proposed approach allows to compute the scaling exponent $\theta$ of the free energy fluctuations as well as the left tail of its probability distribution function. It is argued that $\theta = 1/4$ which is slightly different from the zero-temperature numerical value which is close to $0.241$.