English

Logarithmic superdiffusivity of the 2-dimensional anisotropic KPZ equation

Statistical Mechanics 2020-09-29 v1 Disordered Systems and Neural Networks Mathematical Physics math.MP

Abstract

We study an anisotropic variant of the two-dimensional Kardar-Parisi-Zhang equation, that is relevant to describe growth of vicinal surfaces and has Gaussian, logarithmically rough, stationary states. While the folklore belief (based on one-loop Renormalization Group) is that the equation has the same scaling behaviour as the (linear) Edwards-Wilkinson equation, we prove that, on the contrary, the non-linearity induces the emergence of a logarithmic super-diffusivity. This phenomenon is similar in flavour to the super-diffusivity for two-dimensional fluids and driven particle systems.

Keywords

Cite

@article{arxiv.2009.12934,
  title  = {Logarithmic superdiffusivity of the 2-dimensional anisotropic KPZ equation},
  author = {Giuseppe Cannizzaro and Dirk Erhard and Fabio Toninelli},
  journal= {arXiv preprint arXiv:2009.12934},
  year   = {2020}
}

Comments

5 pages

R2 v1 2026-06-23T18:49:44.613Z