Microscopic interplay of temperature and disorder of a one-dimensional elastic interface

TL;DR

This study numerically investigates how temperature and disorder influence the roughness of a one-dimensional elastic interface, revealing a new short-scale power-law regime and challenging existing theoretical predictions.

Contribution

The paper introduces a numerical analysis of the microscopic interplay between temperature and disorder, identifying a novel short-scale roughness regime with an unexpected exponent.

Findings

Discovery of a new power-law regime at short lengthscales.

Numerical evidence that the disorder roughness exponent is less than 1.

Implications for understanding temperature effects on interface roughness.

Abstract

Elastic interfaces display scale-invariant geometrical fluctuations at sufficiently large lengthscales. Their asymptotic static roughness then follows a power-law behavior, whose associated exponent provides a robust signature of the universality class to which they belong. The associated prefactor has instead a non-universal amplitude fixed by the microscopic interplay between thermal fluctuations and disorder, usually hidden below experimental resolution. Here we compute numerically the roughness of a one-dimensional elastic interface subject to both thermal fluctuations and a quenched disorder with a finite correlation length. We evidence the existence of a novel power-law regime at short lengthscales. We determine the corresponding exponent $\zeta_\textrm{dis}$ and find compelling numerical evidence that, contrarily to available analytic predictions, one has $\zeta_\textrm{dis} < 1$. We discuss the consequences on the temperature dependence of the roughness and the connection with the asymptotic random-manifold regime at large lengthscales. We also discuss the implications of our findings for other systems such as the Kardar-Parisi-Zhang equation and the Burgers turbulence.