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Efficiency Of Parallel Tempering For Ising Systems, Stephan Burkhardt
Efficiency Of Parallel Tempering For Ising Systems, Stephan Burkhardt
Masters Theses 1911 - February 2014
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 …