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  • Open Access

Stationary 1/fγ noise in discrete models of the Kardar-Parisi-Zhang class

Rahul Chhimpa and Avinash Chand Yadav*

  • *Contact author: jnu.avinash@gmail.com
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APS Open Sci. 1, 000168 – Published 9 October, 2026

DOI: https://doi.org/10.1103/mr6f-mj1m

Abstract

In discrete models describing growing rough interfaces in the Kardar-Parisi-Zhang universality class, we examine height fluctuations at a fixed site as a function of time, measured in monolayer units. For small systems, we show that it is possible to reach the stationary state. We compute the two-time autocorrelation and power spectra independently. The correlation function remains nonexponential and vanishes after a correlation time that diverges with system size. As a result, the power spectra display a lower cutoff with constant power. In the nontrivial frequency regime, we observe 1/fγ-type scaling with the spectral exponent 5/3. Finite-size scaling reveals that the temporal correlation function follows dynamic scaling. Our findings, supported by scaling-theoretical arguments, establish that the fluctuations are wide-sense stationary, implying the applicability of the Wiener-Khinchin theorem. The scaling arguments also reveal a scaling relation γ=1+2α/z, where α and z denote the roughness and dynamical exponents.

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APS Open Sci. 1, 000168– Published 9 October, 2026
Vol. 1
  • Received 8 April 2026
  • Revised 31 August 2026
  • Accepted 29 September 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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