Self Consistent Expansion for the Molecular Beam Epitaxy Equation

Abstract

Motivated by a controversy over the correct results derived from the dynamic renormalization group (DRG) analysis of the non linear molecular beam epitaxy (MBE) equation, a self-consistent expansion (SCE) for the non linear MBE theory is considered. The scaling exponents are obtained for spatially correlated noise of the general form $D(\vec{r}-{\vec{r}}^{\prime },t-t^{\prime })=2D_0|\vec{r}-{\vec{r}}^{\prime }{|}^{2\rho -d}\delta (t-t^{\prime })$. I find a lower critical dimension $d_c(\rho )=4+2\rho$, above, which the linear MBE solution appears. Below the lower critical dimension a r-dependent strong-coupling solution is found. These results help to resolve the controversy over the correct exponents that describe non linear MBE, using a reliable method that proved itself in the past by predicting reasonable results for the Kardar-Parisi-Zhang (KPZ) system, where DRG failed to do so.

16 pages

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