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 \pm 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.Comment: 7 pages, 4 figures, published in Europhysics Letters (2005
