Cost of Generalised HMC Algorithms for Free Field Theory

Details Cost of Generalised HMC Algorithms for Free Field Theory Cost of Generalised HMC Algorithms for Free Field Theory

2000-01-28

arxiv.org/abs/hep-lat/0001031v1

Nucl.Phys.Proc.Suppl. 83 (2000) 816-818

Physics

High Energy Physics

High Energy Physics - Lattice

LATTICE99(Algorithms and Machines) - 3 pages, 1 PostScript figure

Scientific paper

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.

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