Exact result vs. dynamic renormalization group analysis for the nonlocal molecular-beam-epitaxy equation

Eytan Katzav*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

9 Scopus citations

Abstract

In this paper, I analyze a generalization of the molecular-beam-epitaxy equation (with spatially correlated noise) that takes into account long-range interactions of a volume conserving surface. This equation is, therefore, called the non-local molecular-beam-epitaxy (NMBE) equation, sometimes also known as the non-local conserved Kardar-Parisi-Zhang equation. I find an exact result for a subfamily of the NMBE models in one dimension. I then compare this exact result to a previous result obtained by Jung et al. (Phys. Rev. E 62 (2000) 2949) who applied a dynamic renormalization group (DRG) analysis to this problem. I show explicitly that this approach does not yield the exact result I obtain. This example suggests that one should be careful when applying DRG to nonlinear continuum equations.

Original languageAmerican English
Pages (from-to)25-28
Number of pages4
JournalPhysica A: Statistical Mechanics and its Applications
Volume308
Issue number1-4
DOIs
StatePublished - 15 May 2002
Externally publishedYes

Keywords

  • Exact result
  • KPZ equation
  • Molecular beam epitaxy
  • Nonlocal models

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