Tuning the hybrid Monte Carlo algorithm

We apply the hybrid Monte Carlo algorithm to pure gauge QCD and to QCD with four flavors of staggered dynamical fermions. We show how the acceptance in the global Metropolis step depends upon the parameters of the algorithm. By tuning the values of the coupling constants in the algorithm to be different from those in the global Metropolis step, we find that the acceptance can be kept large without having to make the step size prohibitively small. We give an analytic discussion of the tuning, and argue that the algorithm requires computer time growing proportional to $V^{5/4}$.