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Width Distributions and the Upper Critical Dimension of KPZ Interfaces

E. Marinari·A. Pagnani·G. Parisi·Z. Racz
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Abstract

Simulations of restricted solid-on-solid growth models are used to build the width-distributions of d=2-5 dimensional KPZ interfaces. We find that the universal scaling function associated with the steady-state width-distribution changes smoothly as d is increased, thus strongly suggesting that d=4 is not an upper critical dimension for the KPZ equation. The dimensional trends observed in the scaling functions indicate that the upper critical dimension is at infinity.

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E. Marinari, A. Pagnani, G. Parisi, Z. Racz. 2001-05-08. Width Distributions and the Upper Critical Dimension of KPZ Interfaces. https://doi.org/10.1103/physreve.65.026136

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