Accelerated simulations of $\mathrm{XY}$ spin glasses

We present numerical simulation results for the $\mathrm{XYq}$ spin-glass model in two and three dimensions, using stochastic differential-equation methods with Fourier acceleration. We show that the dynamics of these methods are much faster than Metropolis and suffer much less from critical slowing down, without changing static quantities. We also show that renormalized physical quantities are not affected by systematic errors. We use this method to show that, in two dimensions, the Ising-type chiral variables of this model follow thermal activation dynamics.