Testing a Variational Approach to Random Directed Polymers

TL;DR

This paper explores a variational method in replica space to analyze one-dimensional directed polymers in random media, confirming known solutions and identifying different regimes based on correlation types.

Contribution

It introduces a variational approach in replica space for directed polymers and compares numerical results with analytic solutions across different correlation regimes.

Findings

Numerical results match known analytic solutions for delta-correlated potentials.

Identifies Flory scaling regime dependent on correlation exponent.

Discovers a short-range regime analogous to delta-correlated case.

Abstract

The one dimensional direct polymer in random media model is investigated using a variational approach in the replica space. We demonstrate numerically that the stable point is a maximum and the corresponding statistical properties for the delta correlated potential are in good agreements with the known analytic solution. In the case of power-law correlated potential two regimes are recovered: a Flory scaling dependent on the exponent of the correlations, and a short range regime in analogy with the delta-correlated potential case.