TY - JOUR

T1 - SCALING IN LANDSCAPE EROSION: RENORMALIZATION GROUP ANALYSIS OF A MODEL WITH INFINITELY MANY COUPLINGS

AU - Antonov, N. V.

AU - Kakin, P. I.

PY - 2017

Y1 - 2017

N2 - 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 β-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, β-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

AB - 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 β-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, β-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

KW - Keywords: turbulence

KW - critical behavior

KW - scaling

KW - renormalization group

U2 - 10.1134/S0040577917020027

DO - 10.1134/S0040577917020027

M3 - Article

VL - 190

SP - 193

EP - 203

JO - Theoretical and Mathematical Physics (Russian Federation)

JF - Theoretical and Mathematical Physics (Russian Federation)

SN - 0040-5779

IS - 2

ER -