Roughening of the anharmonic Larkin model
| Autor: | Víctor Hugo Purrello, Jose Luis Iguain, A. B. Kolton |
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| Rok vydání: | 2018 |
| Předmět: |
Length scale
Ciencias Físicas FOS: Physical sciences Type (model theory) Otras Ciencias Físicas 01 natural sciences 010305 fluids & plasmas Critical phenomena purl.org/becyt/ford/1 [https] 0103 physical sciences 010306 general physics Scaling Brownian motion Mathematical physics Physics Anharmonicity Disordered Systems and Neural Networks (cond-mat.dis-nn) purl.org/becyt/ford/1.3 [https] Condensed Matter - Disordered Systems and Neural Networks Roughness Elasticity Displacement field Thermodynamic limit Exponent Random & disordered media CIENCIAS NATURALES Y EXACTAS |
| Zdroj: | CONICET Digital (CONICET) Consejo Nacional de Investigaciones Científicas y Técnicas instacron:CONICET |
| ISSN: | 2470-0053 |
| Popis: | We study the roughening of $d$-dimensional directed elastic interfaces subject to quenched random forces. As in the Larkin model, random forces are considered constant in the displacement direction and uncorrelated in the perpendicular direction. The elastic energy density contains an harmonic part, proportional to $(\partial_x u)^2$, and an anharmonic part, proportional to $(\partial_x u)^{2n}$, where $u$ is the displacement field and $n>1$ an integer. By heuristic scaling arguments, we obtain the global roughness exponent $\zeta$, the dynamic exponent $z$, and the harmonic to anharmonic crossover length scale, for arbitrary $d$ and $n$, yielding an upper critical dimension $d_c(n)=4n$. We find a precise agreement with numerical calculations in $d=1$. For the $d=1$ case we observe, however, an anomalous "faceted" scaling, with the spectral roughness exponent $\zeta_s$ satisfying $\zeta_s > \zeta > 1$ for any finite $n>1$, hence invalidating the usual single-exponent scaling for two-point correlation functions, and the small gradient approximation of the elastic energy density in the thermodynamic limit. We show that such $d=1$ case is directly related to a family of Brownian functionals parameterized by $n$, ranging from the random-acceleration model for $n=1$, to the L\'evy arcsine-law problem for $n = \infty$. Our results may be experimentally relevant for describing the roughening of non-linear elastic interfaces in a Matheron-de Marsilly type of random flow. Comment: 12 pages, 9 figures, published version |
| Databáze: | OpenAIRE |
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