Critical Dynamics of the Hybrid Monte Carlo Algorithm

We investigate the critical dynamics of the Hybrid Monte Carlo algorithm approaching the chiral limit of standard Wilson fermions. Our observations are based on time series of lengths O(5000) for a variety of observables. The lattice sizes are 16^3 x 32 and 24^3 x 40. We work at beta=5.6, and kappa=0.156, 0.157, 0.1575, 0.158, with 0.83 > m_pi/m_rho > 0.55. We find surprisingly small integrated autocorrelation times for local and extended observables. The dynamical critical exponent $z$ of the exponential autocorrelation time is compatible with 2. We estimate the total computational effort to scale between V^2 and V^2.25 towards the chiral limit.