Analytical study of tunneling times in flat histogram Monte Carlo
Abstract
We present a model for the dynamics in energy space of multicanonical simulation methods that lends itself to a rather complete analytic characterization. The dynamics is completely determined by the density of states. In the ±J 2D spin glass the transitions between the ground state level and the first excited one control the long time dynamics. We are able to calculate the distribution of tunneling times and relate it to the equilibration time of a starting probability distribution. In this model, and possibly in any model in which entering and exiting regions with low density of states are the slowest processes in the simulations, tunneling time can be much larger (by a factor of O(N)) than the equilibration time of the probability distribution. We find that these features also hold for the energy projection of single spin flip dynamics.
 Publication:

EPL (Europhysics Letters)
 Pub Date:
 December 2005
 DOI:
 10.1209/epl/i2005103030
 arXiv:
 arXiv:condmat/0504698
 Bibcode:
 2005EL.....72..802C
 Keywords:

 Condensed Matter  Statistical Mechanics
 EPrint:
 7 pages, 4 figures, published in Europhysics Letters (2005)