Mapping twodimensional surface patterns and scaling onto driven lattice gases
Mapping twodimensional surface patterns and scaling onto driven lattice gases
Odor, G.; Liedke, B.; Heinig, K.H.
We show that a (2+1)dimensional discrete surface growth model exhibiting KardarParisiZhang (KPZ) class scaling can be mapped onto a twodimensional conserved lattice gas model of directed dimers. The KPZ height anisotropy in the surface model corresponds to a driven diusive motion of the lattice gas dimers. We conrm by numerical simulations that the scaling exponents of the dimer model agree with those of the (2+1)dimensional KPZ class. This suggests that the dimension dependence has a topological (exclusion) origin. The mapping opens up the possibility of analyzing growth models via reactiondiusion models and allow much more ecient computer simulations (see [1]). In particular we provide very precise surface scaling exponents for d = 2; 3; 4; 5 dimensions obtained by ecient bitcoded algorithms and discuss the problem of the debated uppercritical dimension of KPZ. Furthermore if we supplement this model with conserved, competing surface diusion reactions we can obtain various, coarsening dot or ripple patterns (see image), which are important in selforganizing nanostructure research (see http://www.iomleipzig.de/for845/).
[1] G. Odor, B. Liedke, and K.H. Heinig, Phys. Rev. E 79 (2009) 021125.
Keywords: KPZ equation; ion erosion; surface pattern formation

Lecture (Conference)
34th Conference of the Middle European Cooperation in Statistical Physics, 30.03.01.04.2009, Leipzig, Germany
Permalink: https://www.hzdr.de/publications/Publ12685
Publ.Id: 12685