Continuous Dimer Angles on the Silicon Surface: Critical Properties and the Kibble-Zurek Mechanism

Abstract

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 $\hat{I}½$ of the symmetry-broken XY model is determined to $\hat{I}½=1.04$. The dynamic critical exponent $z$ is determined to $z=2.13$ and, together with $\hat{I}½$, 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.

8.5+5+2.5 pages, 10 figures, to appear in PRB