Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2003-03-10
Phys. Rev. E 68, 031607 (2003)
Physics
Condensed Matter
Statistical Mechanics
11 pages
Scientific paper
10.1103/PhysRevE.68.031607
In this paper I study a model for a growing surface in the presence of anomalous diffusion, also known as the Fractal Kardar-Parisi-Zhang equation (FKPZ). This equation includes a fractional Laplacian that accounts for the possibility that surface transport is caused by a hopping mechanism of a Levy flight. I show that for a specific choice of parameters of the FKPZ equation, the equation can be solved exactly in one dimension, so that all the critical exponents, which describe the surface that grows under FKPZ, can be derived for that case. Afterwards, I use a Self-Consistent Expansion (SCE) to predict the critical exponents for the FKPZ model for any choice of the parameters and any spatial dimension. It is then verified that the results obtained using SCE recover the exact result in one dimension. At the end a simple picture for the behavior of the Fractal KPZ equation is suggested, and the upper critical dimension of this model is discussed.
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