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 TMF, 2017, Volume 190, Number 2, Pages 226–238 (Mi tmf9147)

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

N. V. Antonov, P. I. Kakin

Saint Petersburg State University, St. Petersburg, Russia

Abstract: Applying the standard field theory renormalization group to the model of landscape erosion introduced by Pastor-Satorras and Rothman yields 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). We show that the one-loop counterterm can nevertheless be expressed in terms of a known function $V(h)$ in the original stochastic equation and its derivatives with respect to the height field $h$. Its Taylor expansion yields the full infinite set of the one-loop renormalization constants, $\beta$-functions, and anomalous dimensions. Instead of a set of fixed points, there arises a two-dimensional surface of fixed points that quite probably contains infrared attractive regions. If that is the case, then the model exhibits scaling behavior in the infrared range. The corresponding critical exponents turn out to be nonuniversal because they depend on the coordinates of the fixed point on the surface, but they satisfy certain universal exact relations.

Keywords: turbulence, critical behavior, scaling, renormalization group

 Funding Agency Grant Number Saint Petersburg State University 11.38.185.2014 Russian Foundation for Basic Research 16-32-00086 This research was supported by St. Petersburg State University (Research Grant No. 11.38.185.2014). The research of P. I. Kakin was also supported by the Russian Foundation for Basic Research (Grant No. 16-32-00086).

DOI: https://doi.org/10.4213/tmf9147

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English version:
Theoretical and Mathematical Physics, 2017, 190:2, 193–203

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Document Type: Article
Revised: 20.01.2016

Citation: N. V. Antonov, P. I. Kakin, “Scaling in landscape erosion: Renormalization group analysis of a model with infinitely many couplings”, TMF, 190:2 (2017), 226–238; Theoret. and Math. Phys., 190:2 (2017), 193–203

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/tmf9147
• https://doi.org/10.4213/tmf9147
• http://mi.mathnet.ru/eng/tmf/v190/i2/p226

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This publication is cited in the following articles:
1. Duclut Ch., Delamotte B., “Nonuniversality in the Erosion of Tilted Landscapes”, Phys. Rev. E, 96:1 (2017), 012149
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