Dynamical critical properties of the hybrid Monte Carlo algorithm

We study the dynamical critical behaviour of the Hybrid Monte Carlo algorithm for the two-dimensional XY model. We observe that randomising trajectory lengths decreases computational effort dramatically in the spin-wave phase, but increases it in the vortex phase. We also find that the dynamical critical exponent is close to 2 in the Langevin limit. When sufficiently long trajectories are used, this exponent drops to 1 in the vortex phase, and to zero in the spin-wave phase. The computational effort in molecular dynamics units, on the other hand, scales with an exponent 1. We present an argument for the generality of this observation