Abstract
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)2470-004510.1103/PhysRevE.99.032105], 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 α_{loc} 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.
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