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arXiv · 1004.2725

Origins of scaling relations in nonequilibrium growth

Carlos Escudero·Elka Korutcheva
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Abstract

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 $α+z=4$, 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 $α+z=4$ 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.

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Carlos Escudero, Elka Korutcheva. 2012-03-14. Origins of scaling relations in nonequilibrium growth. https://arxiv.org/abs/1004.2725

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