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Memory and rejuvenation effects in spin glasses are governed by more than one length scale

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Memory and rejuvenation effects in the magnetic response of off-equilibrium spin glasses have been widely regarded as the doorway into the experimental exploration of ultrametricity and temperature chaos. Unfortunately, despite more than twenty years of theoretical efforts following the experimental discovery of memory and rejuvenation, these effects have, thus far, been impossible to reliably simulate. Yet, three recent developments convinced us to accept this challenge: first, the custom-built Janus II supercomputer makes it possible to carry out simulations in which the very same quantities that can be measured in single crystals of CuMn are computed from the simulation, allowing for a parallel analysis of the simulation and experimental data. Second, Janus II simulations have taught us how numerical and experimental length scales should be compared. Third, we have recently understood how temperature chaos materializes in aging dynamics. All these three aspects have proved crucial for reliably reproducing rejuvenation and memory effects on the computer. Our analysis shows that at least three different length scales play a key role in aging dynamics, whereas essentially all the theoretical analyses of the aging dynamics emphasize the presence and crucial role of a single glassy correlation length.

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Fig. 1: ZFC numerical experiment measuring rejuvenation and memory.
Fig. 2: Temperature chaos is spatially heterogeneous when it is clearly present.
Fig. 3: Aging dynamics is controlled by at least three length scales.
Fig. 4: Strong temperature chaos correlates with full rejuvenation.

Data availability

The data contained in the figures of this paper, accompanied by the gnuplot script files that generate these figures, are publicly available via GitHub at The data that support the findings of this study are available from the corresponding author upon reasonable request.

Code availability

The codes that support the findings of this study are available from the corresponding author upon reasonable request

Change history

  • 23 May 2023

    In the version of this article initially published, call outs to panels in Figure 3, now referring to “left” or “right,” appeared originally as “top” and “bottom”; the callouts have been updated in the HTML and PDF versions of the article.


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We acknowledge the valuable contributions and ideas of our collaborator Raffaele Tripiccione. The Janus project would have been impossible without his technical expertise. We thank R. Orbach for discussions. This work was partly supported by grants nos. PID2020-112936GB-I00, PID2019-103939RB-I00, PGC2018-094684-B-C21, PGC2018-094684-B-C22 and PID2021-125506NA-I00 funded by MCIN/AEI/10.13039/501100011033 by “ERDF A way of making Europe” and by the “European Union; and by the Atracción de Talento program (ref. 2019-T1/TIC-12776) funded by Comunidad de Madrid and Universidad Complutense de Madrid (Spain). This project has received funding from the European Research Council under the European Union’s Horizon 2020 research and innovation programme (grant no. 694925; G.P.). We were also partly supported by ICSC – Centro Nazionale di Ricerca in High Performance Computing, Big Data and Quantum Computing, funded by the European Union – NextGenerationEU. I.G.-A.P. was supported by MCIU (Spain) through FPU grant no. FPU18/02665. J.M.-G. was supported by the Ministerio de Universidades and the European Union ‘NextGenerationEU/PRTR’ through a 2021–2023 Margarita Salas grant. We thank the Spanish Supercomputing Network (RES) for providing access to its Data Storage program at its BIFI (University of Zaragoza) node. IP was supported by LazioInnova-Regione Lazio under the program Gruppi di ricerca2020 - POR FESR Lazio 2014-2020, Project NanoProbe (Application code A0375-2020-36761). BS was partially supported by the Banco Santander and the Complutense University of Madrid through the grant PR44/21-29937.

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Authors and Affiliations



D.I. and A.T. contributed to the design of the Janus II project. J.M.G.-N. and D.N. contributed to the Janus II/Janus simulation software. M.B.-J., E.C., A.C., L.A.F, J.M.G.-N., I.G.-A.P., A.G.-G., D.I., A.M., A.M.S., I.P., S.P.-G., S.F.S. and A.T. contributed to the Janus II hardware and software development. L.A.F., E.M., V.M.-M. and I.P. suggested undertaking this project. L.A.F., E.M., V.M.-M., I.-P., F.R.-T. and J.J.R.-L. designed the research. J.M.-G. and I.P. analysed the data. M.B.-J., L.A.F., E.M., V.M.-M., J.M.-G., I.P., G.P., B.S., J.J.R.-L., F.R.-T. and D.Y. discussed the results. L.A.F., E.M., V.M.-M., J.M.-G., I.P., J.J.R-L., B.S., F.R.-T. and D.Y. wrote the paper.

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Correspondence to I. Paga.

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Baity-Jesi, M., Calore, E., Cruz, A. et al. Memory and rejuvenation effects in spin glasses are governed by more than one length scale. Nat. Phys. 19, 978–985 (2023).

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