Nonlocal growth equations - A test case for dynamic renormalization group analysis

Moshe Schwartz, Eytan Katzav*

*Corresponding author for this work

Research output: Contribution to journalConference articlepeer-review

1 Scopus citations


In this paper we discuss nonlocal growth equations such as the generalization of the Kardar-Parisi-Zhang (KPZ) equation that includes long-range interactions, also known as the Nonlocal-Kardar-Parisi-Zhang (NKPZ) equation, and the nonlocal version of the molecular-beam-epitaxy (NMBE) equation. We show that the steady-state strong coupling solution for nonlocal models such as NKPZ and NMBE can be obtained exactly in one dimension for some special cases, using the Fokker-Planck form of these equations. The exact results we derive do not agree with previous results obtained by Dynamic Renormalization Group (DRG) analysis. This discrepancy is important because DRG is a common method used extensively to deal with nonlinear field equations. While difficulties with this method for d > 1 has been realized in the past, it has been believed so far that DRG is still safe in one dimension. Our result shows differently. The reasons for the failure of DRG to recover the exact one-dimensional results are also discussed.

Original languageAmerican English
Pages (from-to)91-98
Number of pages8
JournalPhysica A: Statistical Mechanics and its Applications
Issue number1-2
StatePublished - 1 Dec 2003
Externally publishedYes
EventRandomes and Complexity - Eilat, Israel
Duration: 5 Jan 20039 Jan 2003


  • Exact result
  • KPZ equation
  • Nonlocal models


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