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

• Published in: arXiv.org
• Main Authors: Caballero, Nirvana, Giamarchi, Thierry, Lecomte, Vivien, Agoritsas, Elisabeth
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 27.05.2022
• Subjects: Physics - Disordered Systems and Neural Networks; Roughness; Temperature dependence
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.2110.13785

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.