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

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 nonuniversal 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 power-law regime at short lengthscales. We determine the corresponding exponent ζ dis and find compelling numerical evidence that, contrarily to available analytic predictions, one has ζ 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.

Degradation of domains with sequential field application

“…The excess roughness due to disorder, compared to bare thermal fluctuations, is described at short length-scales (lower than r 0 ) by a power-law ∼ r ζ dis . We find ζ dis 0.91 and r 0 proportional to the disorder correlation length felt by the interface [47]. A detailed discussion about this is included in a forthcoming paper.…”

“…The disorder correlation length felt by the interface is thus increased, and the region where the 2/3 exponent is observed is pushed to larger scales. An intermediate power-law regime with a larger roughness exponent is then evidenced [47]. This intermediate excess regime is widely explored and studied by us in a forthcoming paper.…”

“…The roughness exponents observed for interfaces under AC cycles is larger compared to the ones observed for interfaces under DC pulses. The length-scales at which the disorder-dominant exponent 2/3 is observed in the roughness function depend, among other factors, on the disorder correlation length [46,47]. When the interface is subjected to AC cycles it is forced to wonder repeatedly trough the same disorder landscape.…”