Kibble-Zurek dynamics in the anisotropic Ising model of the Si(001) surface

Abstract: As a simplified description of the non-equilibrium dynamics of buckled dimers on the Si(001) surface, we consider the anisotropic 2D Ising model and study the freezing of spatial correlations during a cooling quench across the critical point. Depending on the cooling rate, we observe a crossover from 1D to 2D behavior. For rapid cooling, we find effectively 1D behavior in the strongly coupled direction, for which we provide an exact analytic solution of the non-equilibrium dynamics. For slower cooling rates, we start to see 2D behavior where our numerical simulations show an approach to the usual Kibble-Zurek scaling in 2D.