Analytical study of tunneling times in flat histogram Monte Carlo

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

Corresponding author: jlopes@fc.up.pt

Received: 12 August 2005
Accepted: 3 October 2005

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 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 ) than the equilibration time of the probability distribution. We find that these features also hold for the energy projection of single spin flip dynamics.