Markov Chain Monte Carlo Method without Detailed Balance
Abstract
We present a specific algorithm that generally satisfies the balance condition without imposing the detailed balance in the Markov chain Monte Carlo. In our algorithm, the average rejection rate is minimized, and even reduced to zero in many relevant cases. The absence of the detailed balance also introduces a net stochastic flow in a configuration space, which further boosts up the convergence. We demonstrate that the autocorrelation time of the Potts model becomes more than 6 times shorter than that by the conventional Metropolis algorithm. Based on the same concept, a bounce-free worm algorithm for generic quantum spin models is formulated as well.
- Publication:
-
Physical Review Letters
- Pub Date:
- September 2010
- DOI:
- arXiv:
- arXiv:1007.2262
- Bibcode:
- 2010PhRvL.105l0603S
- Keywords:
-
- 05.10.Ln;
- 02.50.-r;
- 02.70.Ss;
- 02.70.Tt;
- Monte Carlo methods;
- Probability theory stochastic processes and statistics;
- Quantum Monte Carlo methods;
- Justifications or modifications of Monte Carlo methods;
- Condensed Matter - Statistical Mechanics;
- Mathematical Physics
- E-Print:
- 5 pages, 5 figures