Publication: Dynamic variational study of chaos: spin glasses in three dimensions
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Publication Date
2018-03-02
Authors
Billoire, A.
Maiorano, A.
Marinari, E.
Moreno Gordo, J.
Parisi, G.
Ricci-Tersenghi, F.
Ruiz Lorenzo, J. J.
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IOP Publishing
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Abstract
We have introduced a variational method to improve the computation of integrated correlation times in the Parallel Tempering Dynamics, obtaining a better estimate (a lower bound, at least) of the exponential correlation time. Using this determination of the correlation times, we revisited the problem of the characterization of the chaos in temperature in finite dimensional spin glasses spin by means of the study of correlations between different chaos indicators computed in the static and the correlation times of the Parallel Tempering dynamics. The sample-distribution of the characteristic time for the Parallel Tempering dynamics turns out to be fat-tailed and it obeys finite-size scaling.
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© 2018 IOP Publishing Ltd and SISSA Medialab srl. We thank the Janus collaboration for allowing us to analyze the L = 32 autocorrelation times from Ref. [21]. We also are grateful for allowing us to carry out a short simulation on the Janus computer, in order to establish the correspondence between the Metropolis and the Heat-bath autocorrelation times. This project has received funding from the European Research Council (ERC) under the European Unions Horizon 2020 research and innovation program (grant agreement No 694925). We were partially supported by MINECO (Spain) through Grant Nos. FIS2015-65078-C2, FIS2016-76359-P and by the Junta de Extremadura (Spain) through Grant No. GRU10158 (these three contracts were partially funded by FEDER). Our simulations were carried out at the BIFI supercomputing center (using the Memento and Cierzo clusters), at the TGCC supercomputing center in Bruyères-le-Châtel (using the Curie computer, under the allocation 2015-056870 made by GENCI) and at ICCAEx supercomputer center in Badajoz (grinfishpc and iccaexhpc). We thank the staff at BIFI, TGCC and ICCAEx supercomputing centers for their assistance.