Numerical analysis of accelerated stochastic algorithms near a critical temperature

We present a numerical study of stochastic differential equations using the XY model in two dimensions as an example. ‘‘Accelerated’’ and ‘‘hybrid’’ algorithms have been implemented and show their advantages over more standard methods. The (partial) evasion of critical slowing down by accelerated algorithms is studied on a sequence of lattices ${16}^2$, ${32}^2$, and ${64}^2$..AE