Directed polymer in random media, in two dimensions: numerical study of the aging dynamics

TL;DR

This paper investigates the aging dynamics of a 1+1 dimensional directed polymer in random media through numerical experiments, revealing behaviors similar to mean field spin glass models and analyzing the phase space landscape.

Contribution

It provides the first detailed numerical study of aging in directed polymers in 1+1 dimensions, connecting their behavior to spin glass models.

Findings

Aging dynamics similar to mean field spin glasses observed

Correlation and overlap functions analyzed

Phase space landscape characterized

Abstract

Following a recent work by Yoshino, we study the aging dynamics of a directed polymer in random media, in 1+1 dimensions. Through temperature quench, and temperature cycling numerical experiments similar to the experiments on real spin glasses, we show that the observed behaviour is comparable to the one of a well known mean field spin glass model. The observation of various quantities (correlation function, ``clonation'' overlap function) leads to an analysis of the phase space landscape.