A variational study of directed polymers in disordered media with short-range interactions

TL;DR

This paper applies a variational method with replica-symmetry breaking to study directed polymers in short-range correlated disordered media across different dimensions, revealing phase behaviors and diffusion properties.

Contribution

It introduces a variational approach capable of handling replica-symmetry breaking for directed polymers with short-range noise, analyzing phase transitions across dimensions.

Findings

In dimensions N<2, only strong-coupling phase and anomalous diffusion are observed.

In dimensions N>2, both weak- and strong-coupling phases are present without anomalous diffusion.

Comparison with power-law correlated noise results highlights differences in phase behavior.

Abstract

A variational method that allows for replica-symmetry breaking is applied to directed polymers in an (N+1)-dimensional disordered medium. The noise studied here has gaussian correlations, i.e. it is short-ranged. In dimensions N<2, the variational scheme yields only a strong-coupling phase and anomalous diffusion; while in dimensions N>2 it shows weak- and strong-coupling phases but no anomalous diffusion. Comparisons are made with the results of Mezard and Parisi [11] for noise with power-law correlations.