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arXiv · 2310.18216

Kibble-Zurek dynamics in the anisotropic Ising model of the Si(001) surface

Gernot Schaller·Friedemann Queisser·Seyedeh Parya Katoorani·Christian Brand·Christian Kohlfürst·Mark R. Freeman·Alfred Hucht·Peter Kratzer·Björn Sothmann·Michael Horn-von Hoegen·Ralf Schützhold
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Abstract

As a simplified description of the non-equilibrium dynamics of buckled dimers on the Si(001) surface, we consider the anisotropic 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 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 non-equilibrium 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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Gernot Schaller, Friedemann Queisser, Seyedeh Parya Katoorani, Christian Brand, Christian Kohlfürst, Mark R. Freeman, Alfred Hucht, Peter Kratzer, Björn Sothmann, Michael Horn-von Hoegen, Ralf Schützhold. 2023-10-27. Kibble-Zurek dynamics in the anisotropic Ising model of the Si(001) surface. https://doi.org/10.1103/rmc4-xqb3

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