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Kibble-Zurek Dynamics in the Anisotropic Ising Model of the Si(001) Surface
G Schaller1, F Queisser1, S P Katoorani1
1Helmholtz-Zentrum Dresden-Rossendorf, Bautzner Landstraße 400, 01328 Dresden, Germany.
Physical Review Letters
|July 31, 2025
Summary
Researchers studied nonequilibrium dynamics using an anisotropic 2D Ising model. They found cooling rate dictates behavior, showing a crossover from 1D to 2D dynamics, with an exact solution for rapid cooling.
Area of Science:
- Condensed Matter Physics
- Surface Science
- Statistical Mechanics
Background:
- The Si(001) surface exhibits complex nonequilibrium dynamics of buckled dimers.
- Understanding these dynamics is crucial for surface science and materials properties.
- Simplified models like the Ising model are often used to capture essential physics.
Purpose of the Study:
- To investigate the nonequilibrium dynamics of buckled dimers on Si(001) using a simplified model.
- To explore the influence of cooling rate on spatial correlation freezing across the critical point.
- To analyze the crossover between one-dimensional (1D) and two-dimensional (2D) behavior.
Main Methods:
- Utilized an anisotropic two-dimensional (2D) Ising model as a simplified representation.
- Studied the freezing of spatial correlations during a cooling quench across the critical point.
- Employed exact analytic solutions for 1D behavior and numerical simulations for 2D behavior.
Main Results:
- Observed a crossover from 1D to 2D behavior depending on the cooling rate.
- Found effectively 1D behavior in the strongly coupled direction for rapid cooling, with an exact analytic solution.
- Numerical simulations indicated an approach to Kibble-Zurek scaling in 2D for slower cooling rates.
Conclusions:
- The cooling rate is a critical parameter determining the dimensionality of nonequilibrium dynamics.
- The anisotropic 2D Ising model effectively captures the crossover between 1D and 2D dynamics.
- Results provide insights into defect formation and scaling laws in quenched systems.
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