Scaling in erosion of landscapes: Renormalization group analysis of a model with infinitely many couplings

Abstract

Standard field theoretic renormalization group is applied to the model of landscape erosion introduced by R. Pastor-Satorras and D. H. Rothman [Phys. Rev. Lett. 80: 4349 (1998); J. Stat. Phys. 93: 477 (1998)] yielding unexpected results: the model is multiplicatively renormalizable only if it involves infinitely many coupling constants ( i.e., the corresponding renormalization group equations involve infinitely many beta-functions). Despite this fact, the one-loop counterterm can be derived albeit in a closed form in terms of the certain function $V(h)$, entering the original stochastic equation, and its derivatives with respect to the height field $h$. Its Taylor expansion gives rise to the full infinite set of the one-loop renormalization constants, beta-functions and anomalous dimensions. Instead of a set of fixed points, there is a two-dimensional surface of fixed points that is likely to contain infrared attractive region(s). If that is the case, the model exhibits scaling behaviour in the infrared range. The corresponding critical exponents are nonuniversal through the dependence on the coordinates of the fixed point on the surface, but satisfy certain universal exact relations.

arXiv commentThe authors thank the Organizers of the International Conference "Models in Quantum Field Theory V" for the opportunity to present the results of the research summarised in the paper

References in corpus (9)

• Scaling of a slope: the erosion of tilted landscapes
• Anisotropic Surface Growth Model in Disordered Media
• Continuum Model for River Networks
• Stochastic equation for the erosion of inclined topography
• Disorder-induced critical behavior in driven diffusive systems
• Strong anisotropy in surface kinetic roughening: analysis and experiments
• Local minimal energy landscapes in river networks
• Strong anisotropy in two-dimensional surfaces with generic scale invariance: Gaussian and related models
• Random interface growth in random environment: Renormalization group analysis of a simple model

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