Microscopic interplay of temperature and disorder of a 1D elastic interface
Résumé
We compute numerically the roughness of a one-dimensional elastic interface subjected 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, resulting from the microscopic interplay between thermal fluctuations and disorder. We determine the corresponding exponent $\zeta_\text{dis}$ and find compelling numerical evidence that, contrarily to available (variational or perturbative) analytic predictions, one has $\zeta_\text{dis} < 1$. 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.