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

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