Cost of Generalised HMC Algorithms for Free Field Theory
High Energy Physics - Lattice
2015-06-25 v1
Abstract
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.
Keywords
Cite
@article{arxiv.hep-lat/0001031,
title = {Cost of Generalised HMC Algorithms for Free Field Theory},
author = {A. D. Kennedy and Brian Pendleton},
journal= {arXiv preprint arXiv:hep-lat/0001031},
year = {2015}
}
Comments
LATTICE99(Algorithms and Machines) - 3 pages, 1 PostScript figure