Hybrid Monte Carlo Algorithm

The Hybrid Monte Carlo Algorithm is a Monte Carlo method for generating systems in the canonical state . The process creates a combination of molecular dynamics and random motion. Molecular dynamics is used to efficiently create new, independent states.

In this process, pseudo-impulses are introduced in order to then numerically solve the equations of motion using the Hamilton function . The pseudo-pulses are initially chosen randomly according to the Gaussian distribution . The new state is then determined by calculating the trajectory in the phase space . Finally, the new state is accepted with the probability . ${\displaystyle P_{\mathrm {A} }=\min \left(1,\exp \left(-{\frac {\Delta H}{kT}}\right)\right)}$

The method is used, for example, in the simulation of non-Abelian gauge theories .

See also

• Metropolis algorithm
• Gibbs sampling

literature

• Richard T. Scalettar, Doug J. Scalapino, and Robert L. Sugar: New algorithm for the numerical simulation of fermions . In: Physical Review B . tape 34 , 1986, ISSN  1538-4489 , pp. 7911 ff .
• Simon Duane, Anthony D. Kennedy, Brian J. Pendleton, and Duncan Roweth: Hybrid Monte Carlo . In: Physics Letters B . tape 195 , 1987, ISSN  0370-2693 , pp. 216-222 .
• Radford M Neal: Handbook of Markov Chain Monte Carlo . 2011, ISBN 0-470-17793-4 , pp. 113-162 ( mcmchandbook.net [PDF]).