  We study analytically the computational cost of the Generalised Hybrid Monte
Carlo (GHMC) algorithm for free field theory. We calculate the autocorrelation
functions of operators quadratic in the fields, and optimise the GHMC momentum
mixing angle, the trajectory length, and the integration stepsize. We show that
long trajectories are optimal for GHMC, and that standard HMC is much more
efficient than algorithms based on the Second Order Langevin (L2MC) or Kramers
Equation. We show that contrary to naive expectations HMC and L2MC have the
same volume dependence, but their dynamical critical exponents are z=1 and
z=3/2 respectively.

High Energy Physics - Lattice