Europhys. Lett.
Volume 72, Number 5, December 2005
Page(s) 802 - 808
Section Condensed matter: electronic structure, electrical, magnetic, and optical properties
Published online 28 October 2005
Europhys. Lett., 72 (5), pp. 802-808 (2005)
DOI: 10.1209/epl/i2005-10303-0

Analytical study of tunneling times in flat histogram Monte Carlo

M. D. Costa1, 2, J. Viana Lopes1, 3 and J. M. B. Lopes dos Santos1

1  Centro de Física do Porto, Departamento de Física, Faculdade de Ciências Universidade do Porto - 4169-007 Porto Portugal
2  Escola Superior de Tecnologia e Gestão, Instituto Politécnico de Viana do Castelo Viana do Castelo, Portugal
3  Departamento de Física, Instituto Superior de Engenharia Instituto Politécnico do Porto - Porto, Portugal

received 12 August 2005; accepted in final form 3 October 2005
published online 28 October 2005

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.

75.10.Hk - Classical spin models.
02.70.Rr - General statistical methods.
64.60.Cn - Order-disorder transformations; statistical mechanics of model systems.

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