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Cost of the Generalised Hybrid Monte Carlo Algorithm for Free Field Theory
| Content Provider | Semantic Scholar |
|---|---|
| Author | Kennedy, A. D. Pendleton, Brian |
| Copyright Year | 2001 |
| 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. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://www.ph.ed.ac.uk/~adk/exact.pdf |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Autocorrelation Computational complexity theory Dynamical system Hybrid Memory Cube Hybrid Monte Carlo Leapfrog integration Metropolis Molecular dynamics Monte Carlo algorithm Monte Carlo method Polynomial Quantum field theory Two-Hybrid System Techniques |
| Content Type | Text |
| Resource Type | Article |
