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Access Type
Open Access
Document Type
thesis
Degree Program
Physics
Degree Type
Master of Science (M.S.)
Year Degree Awarded
2010
Month Degree Awarded
September
Keywords
Monte Carlo, Parallel Tempering, Replica Exchange, Ising
Abstract
The efficiency of parallel tempering Monte Carlo is studied for a two-dimensional Ising system of length L with N=L^2 spins. An external field is used to introduce a difference in free energy between the two low temperature states.
It is found that the number of replicas R_opt that optimizes the parallel tempering algorithm scales as the square root of the system size N. For two symmetric low temperature states, the time needed for equilibration is observed to grow as L^2.18. If a significant difference in free energy is present between the two states, this changes to L^1.02.
It is therefore established that parallel tempering is sped up by a factor of roughly L if an asymmetry is introduced between the low temperature states. This confirms previously made predictions for the efficiency of parallel tempering. These findings should be especially relevant when using parallel tempering for systems like spin glasses, where no information about the degeneracy of low temperature states is available prior to the simulation.
DOI
https://doi.org/10.7275/1467366
First Advisor
Jonathan Machta
Second Advisor
Christian Santangelo