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Scaling regimes and critical dimensions in the Kardar-Parisi-Zhang problem

Erwin Frey·Uwe C. T"auber·Hans-Karl Janssen
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Abstract

We study the scaling regimes for the Kardar-Parisi-Zhang equation with noise correlator R(q) ~ (1 + w q^{-2 ρ}) in Fourier space, as a function of ρand the spatial dimension d. By means of a stochastic Cole-Hopf transformation, the critical and correction-to-scaling exponents at the roughening transition are determined to all orders in a (d - d_c) expansion. We also argue that there is a intriguing possibility that the rough phases above and below the lower critical dimension d_c = 2 (1 + ρ) are genuinely different which could lead to a re-interpretation of results in the literature.

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Erwin Frey, Uwe C. T"auber, Hans-Karl Janssen. 1999-04-19. Scaling regimes and critical dimensions in the Kardar-Parisi-Zhang problem. https://doi.org/10.1209/epl%2Fi1999-00343-4

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