Nonuniversality of critical exponents in a fractional quenched Kardar-Parisi-Zhang equation. (English) Zbl 1291.82089
Summary: In this article we address the problem of the depinning transition for driven interfaces in random media. We introduce a fractional Kardar-Parisi-Zhang equation with quenched noise, in which the normal diffusion term is replaced by a fractional Laplacian accounting for long-range interactions through quenched disorder. The critical values of the external driving force and nonlinear term coefficient evidently depend on the system size at the depinning transition. For a fixed value of the external driving force, the fractional order much determines the value of the nonlinear term coefficient that leads to a depinned interface. Near the depinning threshold, the critical exponent obtained numerically is nonuniversal, and weakly depends on the fractional order.
MSC:
| 82C24 | Interface problems; diffusion-limited aggregation in time-dependent statistical mechanics |
| 82C27 | Dynamic critical phenomena in statistical mechanics |
| 35Q53 | KdV equations (Korteweg-de Vries equations) |
| 35B33 | Critical exponents in context of PDEs |
| 35R11 | Fractional partial differential equations |
Keywords:
universality class; depinning transition; critical exponents; fractional Kardar-Parisi-Zhang equationReferences:
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