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

Eytan Katzav·Moshe Schwartz
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Abstract

The controversy whether or not he 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 variuos authors that 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 expansion that indeed there exist a UCD and then obtain it numerically by properly defining the integrals involved.

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Eytan Katzav, Moshe Schwartz. 2001-04-06. Existence of the upper critical dimension of the Kardar-Parisi-Zhang equation. https://doi.org/10.1016/s0378-4371(02)00553-8

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