On the scaling properties of (2+1) directed polymers in the high temperature limit

TL;DR

This paper investigates the high temperature behavior of (2+1) directed polymers in a random potential, proposing a method to compute free energy fluctuation exponents and showing their temperature dependence, indicating non-universality.

Contribution

It introduces a novel approach using the replica method to analyze the high temperature limit and computes the free energy fluctuation exponent for (2+1) directed polymers.

Findings

The scaling exponent $ heta$ is approximately 1/2 at high temperature.

The exponent differs from the zero-temperature value, indicating temperature dependence.

The free energy distribution's left tail is characterized in this regime.

Abstract

In this paper in terms of the replica method we consider the high temperature limit of (2+1) directed polymers in a random potential and propose an approach which 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 $\theta = 1/2$ which is different from the zero-temperature numerical value which is close to 0.241. This result implies that unlike the $(1+1)$ system in the two-dimensional case the free energy scaling exponent is non-universal being temperature dependent.