Roughening of the anharmonic elastic interface in correlated random media

ALÉS, ALEJANDRO; LÓPEZ, JUAN M.

Physical Review E

American Physical Society

Año: 2021 vol. 104

2470-0045

We study the roughening properties of the anharmonic elastic interface in the presence of temporally correlated noise. The model can be seen as a generalization of the anharmonic Larkin model, recently introduced by Purrello, Iguain, and Kolton [Phys. Rev. E 99, 032105 (2019)], to investigate the effect of higher-order corrections to linear elasticity in the fate of interfaces. We find analytical expressions for the critical exponents as a  function of the anharmonicity index n, the noise correlator range θ ∈ [0, 1/2], and dimension d . In d = 1 we find that the interface becomes faceted and exhibits anomalous scaling for θ > 1/4 for any degree of  anharmonicity n > 1. Analytical expressions for the anomalous exponents αloc and κ are obtained and compared with a numerical integration of the model. Our theoretical results show that anomalous roughening cannot exist for this model in dimensions d > 1.