Existence of the upper critical dimension of the Kardar-Parisi-Zhang equation

Eytan Katzav, Moshe Schwartz*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

25 Scopus citations


The controversy whether or not the Kardar-Parisi-Zhang (KPZ) equation has an upper critical dimension (UCD) is going on for quite a long time. Some approximate integral equations for the two-point function served as an indication for the existence of a UCD, by obtaining a dimension, above which the equation does not have a strong coupling solution. A surprising aspect of these studies, however, is that various authors who considered the same equation produced large variations in the UCD. This caused some doubts concerning the existence of a UCD. Here we revisit these calculations, describe the reason for such large variations in the results of identical calculations, show by a large-d asymptotic expansion that indeed there exists a UCD and then obtain it numerically by properly defining the integrals involved. Since many difficult problems in condensed matter physics of non-linear nature are handled with mode-coupling and self-consistent theories, this work might also contribute to other researchers working on a large class of different problems that might run into the same inconsistencies.

Original languageAmerican English
Pages (from-to)69-78
Number of pages10
JournalPhysica A: Statistical Mechanics and its Applications
Issue number1-2
StatePublished - 1 Jun 2002
Externally publishedYes


  • KPZ equation
  • Upper critical dimension


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