Continuous Dimer Angles on the Silicon Surface: Critical Properties and the Kibble-Zurek Mechanism
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909425053204480 |
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| author | Weitzel, Andreas Schaller, Gernot Queisser, Friedemann Schützhold, Ralf |
| author_facet | Weitzel, Andreas Schaller, Gernot Queisser, Friedemann Schützhold, Ralf |
| contents | Langevin dynamics simulations are used to analyze the static and dynamic properties of an {XY} model adapted to dimers forming on Si(001) surfaces. The numerics utilise high-performance parallel computation methods on GPUs. The static exponent $ν$ of the symmetry-broken XY model is determined to $ν= 1.04$. The dynamic critical exponent $z$ is determined to $z = 2.13$ and, together with $ν$, shows the behavior of the Ising universality class. For time-dependent temperatures, we observe frozen domains and compare their size distribution with predictions from Kibble-Zurek theory. We determine a significantly larger quench exponent that shows little dependence on the damping or the symmetry-breaking field. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2409_06412 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Continuous Dimer Angles on the Silicon Surface: Critical Properties and the Kibble-Zurek Mechanism Weitzel, Andreas Schaller, Gernot Queisser, Friedemann Schützhold, Ralf Statistical Mechanics Materials Science Langevin dynamics simulations are used to analyze the static and dynamic properties of an {XY} model adapted to dimers forming on Si(001) surfaces. The numerics utilise high-performance parallel computation methods on GPUs. The static exponent $ν$ of the symmetry-broken XY model is determined to $ν= 1.04$. The dynamic critical exponent $z$ is determined to $z = 2.13$ and, together with $ν$, shows the behavior of the Ising universality class. For time-dependent temperatures, we observe frozen domains and compare their size distribution with predictions from Kibble-Zurek theory. We determine a significantly larger quench exponent that shows little dependence on the damping or the symmetry-breaking field. |
| title | Continuous Dimer Angles on the Silicon Surface: Critical Properties and the Kibble-Zurek Mechanism |
| topic | Statistical Mechanics Materials Science |
| url | https://arxiv.org/abs/2409.06412 |