Dear Prof. Troyer,
I understand that the correlation time tau in the MC classical simulation could be large if we are far from the critical point. However I run simulations for the Ising and for the O(2) model at the critical point and the result for the tau value of the energy density is always large: Three dimensional XY model at T_c=2.201838 32^3 spin Energy Density: -0.9983644 +/- 0.000187, count=2000055, tau=92.3 40^3 spin Energy Density: -0.9953844 +/- 0.000157, count=2000053, tau=118 The same holds, more or less, for the three-dimensional Ising model at T_c=4.511523378 32^3 spins Energy Density: -1.007205 +/- 0.000234, count=2000576, tau=39 40^3 spins Energy Density: -1.003058 +/- 0.000196, count=2000101, tau=49.8 Here tau is lower than in the O(2) case, but still >>1.
Why do you think it remains so large?
Thank you very much for your kind help,
Rachele Nerattini
2014-10-22 14:10 GMT+02:00 Rachele Nerattini r.nerattini@gmail.com:
Dear Prof. Troyer,
thank you very much for the quick answer, I see the point.
All the best
Rachele Nerattini
2014-10-22 14:07 GMT+02:00 Matthias Troyer troyer@phys.ethz.ch:
We do single cluster Wolff-like updates. Hence if you are not close to the critical point the clusters are small and only few spins get updated. This makes for fast sweeps but longer autocorrelation times for the energy.
Matthias
On 22 Oct 2014, at 08:01, Rachele Nerattini r.nerattini@gmail.com wrote:
Dear ALPS community,
I am writing for a question on the algorithm for classical Monte Carlo simulation of spin models. From the simulations I performed on classical O(2), O(3) and O(4) models it turned out that the autocorrelation time is quite large, let's say of about 80 o 90, for the energy density observable. I just would like to understand better if there is a particular reason for such a big tau and which kind of algorithm is really used for the simulation: Swendsen-Wang , Wolff single cluster or even something else? This is also because the term ”sweep” is quite unusual when cluster algorithms are concerned.
I really thank you all for your help.
Best regards,
Rachele Nerattini
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Rachele Nerattini Dip. di Fisica e Astronomia, Università di Firenze Via G. Sansone, 1, 50019 Sesto Fiorentino (FI), Italy
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Rachele Nerattini Dip. di Fisica e Astronomia, Università di Firenze Via G. Sansone, 1, 50019 Sesto Fiorentino (FI), Italy