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

TL;DR

This study uses GPU-accelerated Langevin dynamics to analyze the critical behavior of an XY model on silicon surfaces, revealing Ising universality and validating Kibble-Zurek predictions for domain formation during quenches.

Contribution

It provides the first detailed numerical analysis of the static and dynamic critical properties of dimer arrangements on Si(001) surfaces, including critical exponents and domain size distributions.

Findings

Static exponent ν ≈ 1.04 indicating Ising universality.

Dynamic exponent z ≈ 2.13 consistent with Ising class.

Frozen domain size distributions match Kibble-Zurek theory predictions.

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 $\nu$ 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.