Origins of scaling relations in nonequilibrium growth

Details Origins of scaling relations in nonequilibrium growth Origins of scaling relations in nonequilibrium growth

2010-04-15

arxiv.org/abs/1004.2725v4

J. Phys. A: Math. Theor. 45 (2012) 125005

Physics

Condensed Matter

Statistical Mechanics

Scientific paper

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.

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