2001/07/31 by Eytan Katzav · 2 citations
Physics and Astronomy · #Physics of Superconductivity and Magnetism #Spectroscopy and Quantum Chemical Studies #Theoretical and Computational Physics #cond-mat.mtrl-sci #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.65.032103
published as Phys. Rev. E 65, 032103 (2002) · 16 pages
arxiv created 2001/11/30 · openalex publication_date 2002/02/27 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Motivated by a controversy over the correct results derived from the dynamic renormalization group (DRG) analysis of the nonlinear molecular beam epitaxy (MBE) equation, a self-consistent expansion for the nonlinear MBE theory is considered. The scaling exponents are obtained for spatially correlated noise of the general form D(\stackrel\ensuremath→r\ensuremath-r^\ensuremath',t\ensuremath-t^\ensuremath')=2D0|\stackrel\ensuremath→r\ensuremath-r^\ensuremath'|^2\ensuremathρ\ensuremath-d\ensuremathδ(t\ensuremath-t^\ensuremath'). I find a lower critical dimension dc(\ensuremathρ)=4+2\ensuremathρ, above which the linear MBE solution appears. Below the lower critical dimension a \ensuremathρ-dependent strong-coupling solution is found. These results help to resolve the controversy over the correct exponents that describe nonlinear MBE, using a reliable method that proved itself in the past by giving reasonable results for the strong-coupling regime of the Kardar-Parisi-Zhang system (for d>1), where DRG failed to do so.