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The Upper Critical Dimension of the KPZ Equation

Michael Lassig·Harald Kinzelbach
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Abstract

The strong-coupling regime of Kardar-Parisi-Zhang surface growth driven by short-ranged noise has an upper critical dimension d_> less or equal to four (where the dynamic exponent z takes the value z (d_>) = 2). To derive this, we use the mapping onto directed polymers with quenched disorder. Two such polymers coupled by a small contact attraction are shown to form a bound state at all temperatures below the roughening temperature of a single polymer. Comparing the singularities of the localization length at and below the critical temperature yields d_> \leq 4.

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Michael Lassig, Harald Kinzelbach. 1996-08-22. The Upper Critical Dimension of the KPZ Equation. https://arxiv.org/abs/cond-mat/9608099

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