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Kibble-Zurek Dynamics in the Anisotropic Ising Model of the Si(001) Surface

G. Schaller1, F. Queisser1, S. P. Katoorani1, C. Brand2, C. Kohlfürst1, M. R. Freeman3, A. Hucht2, P. Kratzer2, B. Sothmann2 et al.

M. Horn-von Hoegen2 and R. Schützhold1,4

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Phys. Rev. Lett. 134, 246202 – Published 17 June, 2025

DOI: https://doi.org/10.1103/rmc4-xqb3

Abstract

As a simplified description of the nonequilibrium dynamics of buckled dimers on the Si(001) surface, we consider the anisotropic two-dimensional (2D) Ising model and study the freezing of spatial correlations during a cooling quench across the critical point. Depending on the cooling rate, we observe a crossover from one-dimensional (1D) to 2D behavior. For rapid cooling, we find effectively 1D behavior in the strongly coupled direction, for which we provide an exact analytic solution of the nonequilibrium dynamics. For slower cooling rates, we start to see 2D behavior where our numerical simulations show an approach to the usual Kibble–Zurek scaling in 2D.

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Phys. Rev. Lett. 134, 246202– Published 17 June, 2025
  • Received 1 July 2024
  • Revised 27 January 2025
  • Accepted 15 May 2025
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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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