Origins of scaling relations in nonequilibrium growth

Scaling and hyperscaling laws provide exact relations among critical exponents describing the behavior of a system at criticality. For nonequilibrium growth models with a conserved drift there exist few of them. One such relation is \(\alpha +z=4\), found to be inexact in a renormalization group cal...

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Bibliographic Details
Published inarXiv.org
Main Authors Escudero, Carlos, Korutcheva, Elka
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 14.03.2012
Subjects
Growth models
Scaling laws
Two dimensional models
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Summary:Scaling and hyperscaling laws provide exact relations among critical exponents describing the behavior of a system at criticality. For nonequilibrium growth models with a conserved drift there exist few of them. One such relation is \(\alpha +z=4\), found to be inexact in a renormalization group calculation for several classical models in this field. Herein we focus on the two-dimensional case and show that it is possible to construct conserved surface growth equations for which the relation \(\alpha +z=4\) is exact in the renormalization group sense. We explain the presence of this scaling law in terms of the existence of geometric principles dominating the dynamics.
ISSN:2331-8422