Cost of the generalized hybrid Monte Carlo algorithm for free field theory

Kennedy, A.D.; Pendleton, Brian

doi:10.1016/S0550-3213(01)00129-8

Cost of the generalized hybrid Monte Carlo algorithm for free field theory

A.D. Kennedy
(
- Edinburgh U.
)
,
Brian Pendleton
(
- Edinburgh U.
)

Aug, 2000

54 pages

Published in:

Nucl.Phys.B 607 (2001) 456-510

e-Print:

hep-lat/0008020 [hep-lat]

DOI:

10.1016/S0550-3213(01)00129-8

Report number:

EDINBURGH-2000-16

View in:

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Abstract:

We study analytically the computational cost of the Generalised Hybrid Monte Carlo (GHMC) algorithm for free field theory. We calculate the Metropolis acceptance probability for leapfrog and higher-order discretisations of the Molecular Dynamics (MD) equations of motion. We show how to calculate autocorrelation functions of arbitrary polynomial operators, and use these to optimise the GHMC momentum mixing angle, the trajectory length, and the integration stepsize for the special cases of linear and quadratic operators. We show that long trajectories are optimal for GHMC, and that standard HMC is more efficient than algorithms based on Second Order Langevin Monte Carlo (L2MC), sometimes known as 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.

Note:

54 pages, 3 figures Report-no: Edinburgh 2000/16

12.38.Gc
11.15.Ha
02.70.Lq
Hybrid Monte Carlo (HMC)
GHMC
Molecular dynamics
Field theory
Lattice field theory
lattice field theory
field theory: scalar

References(24)

Figures(0)

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Cost of the generalized hybrid Monte Carlo algorithm for free field theory

Citations per year

Hybrid Monte Carlo

Tuning the generalized hybrid Monte Carlo algorithm

Cost of generalized HMC algorithms for free field theory

Nonreversibility of molecular dynamics trajectories

Instabilities and nonreversibility of molecular dynamics trajectories

The Local hybrid Monte Carlo algorithm for free field theory: Reexamining overrelaxation

Instability in the molecular dynamics step of hybrid Monte Carlo in dynamical Fermion lattice QCD simulations

PROGRAM FOR EFFICIENT MONTE CARLO COMPUTATIONS OF QUENCHED SU(3) LATTICE GAUGE THEORY USING THE QUASI - HEAT BATH METHOD ON A CDC-CYBER-205 COMPUTER

A Generalized guided Monte Carlo algorithm

The Kramers equation simulation algorithm. 1. Operator analysis

Stochastic Quantization in Phase Space

The second order Langevin equation and numerical simulations

New Algorithm for the Numerical Simulation of Fermions

An Improved Hybrid Monte Carlo Method

A Comparison of Numerical Algorithms for Dynamical Fermions

HIGHER ORDER HYBRID MONTE CARLO ALGORITHMS

REMARKS ON GLOBAL MONTE CARLO ALGORITHMS

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Parallel tempering in lattice QCD with O(a)-improved Wilson fermions

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QCD beta function with two flavors of dynamical Wilson fermions