Width distributions and the upper critical dimension of Kardar-Parisi-Zhang interfaces

2001/05/08 by E. Marinari, Enzo Marinari, A. Pagnani +5 · 1 citation
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Complex Systems and Time Series Analysis #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.stat-mech

paper · pdf · doi:10.1103/physreve.65.026136

published as Phys. Rev. E 65, 026136 (2002) · 4 pages, 4 postscript figures, RevTex

arxiv created 2001/05/08 · openalex publication_date 2002/01/23 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Simulations of restricted solid-on-solid growth models are used to build the width distributions of d=2-5 dimensional Kardar-Parisi-Zhang (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.

Citations

• From Massively Parallel Algorithms and Fluctuating Time Horizons to Nonequilibrium Surface Growth
• Critical exponents of the KPZ equation via multi-surface coding numerical simulations
• Magnetic fluctuations in the classicalXYmodel: The origin of an exponential tail in a complex system
• Scaling regimes and critical dimensions in the Kardar-Parisi-Zhang problem

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