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©2022 American Physical Society The authors wish to thank the Janus Collaboration for allowing us to analyze their data. We would like also to thank E. Marinari for interesting discussions. The analysis of the Janus configurations was performed at the ICCAEx Supercomputer Center in Badajoz, and we thank its staff for their assistance. This work was supported by the European Research Council under the European Unions Horizon 2020 Research and Innovation Programme (Grant No. 694925, G.P.), by Ministerio de Economía y Competitividad, Agencia Estatal de Investigación, and Fondo Europeo de Desarrollo Regional(FEDER)(Spain and European Union) through Grants No. PID2020-112936GB-I00 and No. PGC2018-094684-B-C21, and by Junta de Extremadura (Spain) through Grants No. GRU18079 and No. IB20079 (partially funded by FEDER). I.G.A.P. was supported by MCIU (Spain) through FPU Grant No. FPU18/02665., A growing body of evidence indicates that the sluggish low-temperature dynamics of glass formers (e.g., supercooled liquids, colloids, or spin glasses) is due to a growing correlation length. Which is the effective field theory that describes these correlations? The natural field theory was drastically simplified by Bray and Roberts in 1980. More than 40 years later, we confirm the tenets of Bray and Roberts’s theory by studying the Ising spin glass in an externally applied magnetic field, both in four spatial dimensions (data obtained from the Janus collaboration) and on the Bethe lattice., Unión Europea. Horizonte 2020, Ministerio de Economia, Industria y Competitividad (MINECO)/FEDER, Ministerio de Ciencia e Innovación (MICINN), Junta de Extremadura /FEDER, Depto. de Física Teórica, Fac. de Ciencias Físicas, TRUE, pub

© The Author(s) 2021 Artículo publicado por más de 10 autores. We are grateful for discussions with R. Orbach and Q. Zhai. This work was partially supported by Ministerio de Economia, Industria y Competitividad (MINECO, Spain), Agencia Estatal de Investigacion (AEI, Spain), and Fondo Europeo de Desarrollo Regional (FEDER, EU) through Grants No. FIS2016-76359-P, No. PID2019-103939RB-I00, No. PGC2018-094684-B-C21 and PGC2018-094684-B-C22, by the Junta de Extremadura (Spain) and Fondo Europeo de Desarrollo Regional (FEDER, EU) through Grant No. GRU18079 and IB15013 and by the DGA-FSE (Diputacion General de Aragon - Fondo Social Europeo). This project has also received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation program (Grant No. 694925-LotglasSy). DY was supported by the Chan Zuckerberg Biohub and IGAP was supported by the Ministerio de Ciencia, Innovacion y Universidades (MCIU, Spain) through FPU grant no. FPU18/02665. BS was supported by the Comunidad de Madrid and the Complutense University of Madrid (Spain) through the Atraccion de Talento program (Ref. 2019-T1/TIC-12776)., Experiments featuring non-equilibrium glassy dynamics under temperature changes still await interpretation. There is a widespread feeling that temperature chaos (an extreme sensitivity of the glass to temperature changes) should play a major role but, up to now, this phenomenon has been investigated solely under equilibrium conditions. In fact, the very existence of a chaotic effect in the non-equilibrium dynamics is yet to be established. In this article, we tackle this problem through a large simulation of the 3D Edwards-Anderson model, carried out on the Janus II supercomputer. We find a dynamic effect that closely parallels equilibrium temperature chaos. This dynamic temperature-chaos effect is spatially heterogeneous to a large degree and turns out to be controlled by the spin-glass coherence length xi. Indeed, an emerging length-scale xi* rules the crossover from weak (at xi MUCH LESS-THAN xi*) to strong chaos (xi >> xi*). Extrapolations of xi* to relevant experimental conditions are provided. While temperature chaos is an equilibrium notion that denotes the extreme fragility of the glassy phase with respect to temperature changes, it remains unclear whether it is present in non-equilibrium dynamics. Here the authors use the Janus II supercomputer to prove the existence of dynamic temperature chaos, a nonequilibrium phenomenon that closely mimics equilibrium temperature chaos., Unión Europea. Horizonte 2020, Ministerio de Economia, Industria y Competitividad (MINECO)/FEDER, Ministerio de Ciencia e Innovación (MICCIN), Comunidad de Madrid/Universidad Complutense de Madrid, Junta de Extremadura /FEDER, Chan Zuckerberg Biohub, Depto. de Física Teórica, Fac. de Ciencias Físicas, TRUE, pub

© the author(s) This work was partially supported by Ministerio de Economía, Industria y Competitividad (MINECO, Spain), Agencia Estatal de Investigación (AEI, Spain), and Fondo Europeo de Desarrollo Regional (FEDER, EU) through Grants No. PGC2018-094684-B-C21, No. FIS2017-84440-C2-2-P, and No. MTM2017-84446-C2-2-R. A.L. and J.S. were also partially supported by Grant No. PID2020-116567GB-C22 AEI/10.13039/501100011033. A.L. was also partly supported by Grant No A-FQM-644-UGR20 Programa operativo FEDER Andalucía 2014–2020. J.S. was also partly supported by the Madrid Government (Comunidad de Madrid-Spain) under the Multiannual Agreement with UC3M in the line of Excellence of University Professors (EPUC3M23), and in the context of the V PRICIT (Regional Programme of Research and Technological Innovation). I.G.-A.P. was supported by the Ministerio de Ciencia, Innovación y Universidades (MCIU, Spain) through FPU Grant No. FPU18/02665., Cooling and heating faster a system is a crucial problem in science, technology, and industry. Indeed, choosing the best thermal protocol to reach a desired temperature or energy is nota trivial task. Noticeably, we find that the phase transitions may speed up thermalization in systems where there are no conserved quantities. In particular, we show that the slow growth of magnetic domains shortens the overall time that the system takes to reach a final desired state. To prove that statement, we use intensive numerical simulations of a prototypical many-body system, namely, the two-dimensional Ising model., Ministerio de Economía, Industria y Competitividad (MINECO)/FEDER, Ministerio de Economía, Industria y Competitividad (MINECO)/AEI, Ministerio de Ciencia e Innovación (MICCIN), Junta de Andalucía/FEDER, Comunidad de Madrid/Universidad Carlos III de Madrid, Depto. de Física Teórica, Fac. de Ciencias Físicas, TRUE, pub

© 2021 IOP Publishing Ltd We are grateful for helpful discussions with S Swinnea about sample characterisation. This work was partially supported by the US Department of Energy, Office of Basic Energy Sciences, Division of Materials Science and Engineering, under Award No. DE-SC0013599, and Contract No. DE-AC02-07CH11358. We were partly funded as well by Ministerio de Economia, Industria y Competitividad (MINECO, Spain), Agencia Estatal de Investigacion (AEI, Spain), and Fondo Europeo de Desarrollo Regional (FEDER, EU) through Grants No. FIS2016-76359-P, No. PID2019-103939RB-I00, No. PGC2018-094684-B-C21 and PGC2018-094684-B-C22, by the Junta de Extremadura (Spain) and Fondo Europeo de Desarrollo Regional (FEDER, EU) through Grant Nos. GRU18079 and IB15013 and by the DGA-FSE (Diputaci ' on General de Aragon-Fondo Social Europeo). This project has also received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (Grant No. 694925 LotGlasSy). D Y was supported by the Chan Zuckerberg Biohub and IGAP was supported by the Ministerio de Ciencia, Innovacion y Universidades (MCIU, Spain) through FPU Grant No. FPU18/02665. B S was supported by the Comunidad de Madrid and the Complutense University of Madrid (Spain) through the Atraccion de Talento programme (reference 2019-T1/TIC-12776). The simulations of section 5.6.2 were carried out at the ICCAEx supercomputer centre in Badajoz. We thank the staff at ICCAEx for their assistance., The synergy between experiment, theory, and simulations enables a microscopic analysis of spin-glass dynamics in a magnetic field in the vicinity of and below the spin-glass transition temperature T-g. The spin-glass correlation length, xi(t, t(w); T), is analysed both in experiments and in simulations in terms of the waiting time t(w) after the spin glass has been cooled down to a stabilised measuring temperature T < T-g and of the time t after the magnetic field is changed. This correlation length is extracted experimentally for a CuMn 6 at. % single crystal, as well as for simulations on the Janus II special-purpose supercomputer, the latter with time and length scales comparable to experiment. The non-linear magnetic susceptibility is reported from experiment and simulations, using xi(t, t(w); T) as the scaling variable. Previous experiments are reanalysed, and disagreements about the nature of the Zeeman energy are resolved. The growth of the spin-glass magnetisation in zero-field magnetisation experiments, M-ZFC(t, t(w); T), is measured from simulations, verifying the scaling relationships in the dynamical or non-equilibrium regime. Our preliminary search for the de Almeida-Thouless line in D = 3 is discussed., Unión Europea. Horizonte 2020, Ministerio de Economia, Industria y Competitividad (MINECO)/AEI/FEDER, Ministerio de Ciencia e Innovación (MICCIN), Comunidad de Madrid/Universidad Complutense de Madrid, Junta de Extremadura /FEDER, United States Department of Energy (DOE), Depto. de Física Teórica, Fac. de Ciencias Físicas, TRUE, pub

© 2020 American Physical Society. Artículo publicado por más de 10 autores. We are grateful for helpful discussions with S. Swinnea about sample characterization. This work was partially supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Science and Engineering, under Award No. DE-SC0013599, and Contract No. DE-AC02-07CH11358; by the Ministerio de Economia, Industria y Competitividad (MINECO, Spain), Agencia Estatal de Investigacion (AEI, Spain), and Fondo Europeo de Desarrollo Regional (FEDER, EU) through Grants No. FIS2016-76359-P, No. PID2019-103939RB-I00, No. PGC2018-094684-B-C21, and No. PGC2018-094684-B-C22; by the Junta de Extremadura (Spain) and Fondo Europeo de Desarrollo Regional (FEDER, EU) through Grants No. GRU18079 and No. IB15013. This project has also received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation program (Grant No. 694925-LotglasSy). D. Y. was supported by the Chan Zuckerberg Biohub and I. G. A. P. was supported by the Ministerio de Ciencia, Innovacion y Universidades (MCIU, Spain) through FPU Grant No. FPU18/02665. B. S. was supported by the Comunidad de Madrid and the Complutense University of Madrid (Spain) through the Atraccion de Talento program (Ref. 2019-T1/TIC-12776)., The correlation length xi, a key quantity in glassy dynamics, can now be precisely measured for spin glasses both in experiments and in simulations. However, known analysis methods lead to discrepancies either for large external fields or close to the glass temperature. We solve this problem by introducing a scaling law that takes into account both the magnetic field and the time-dependent spin-glass correlation length. The scaling law is successfully tested against experimental measurements in a CuMn single crystal and against large-scale simulations on the Janus II dedicated computer., Unión Europea. Horizonte 2020, Ministerio de Economía y Competitividad (MINECO)/FEDER, Ministerio de Ciencia e Innovación (MICCIN), Comunidad de Madrid/Universidad Complutense de Madrid, Junta de Extremadura /FEDER, United States Department of Energy (DOE), Depto. de Física Teórica, Fac. de Ciencias Físicas, TRUE, pub

©2019 IOP Publishing We thank E Marinari, D Yllanes and F Ladieu for encouraging discussions. This work was partially supported by Ministerio de Economia, Industria y Competitividad (MINECO) Grants No. FIS2015-65078-C2, No. FIS2016-76359-P (both partly funded by FEDER). We were also partly funded by the Junta de Extremadura (Spain) through Grants No. GRU10158 and IB1603 (partially funded by FEDER). This project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation program (Grant No. 694925 GlassUniversality)., We study the problem of glassy relaxations in the presence of an external field in the highly controlled context of a spin-glass simulation. We consider a small spin glass in three dimensions (specifically, a lattice of size L = 8, small enough to be equilibrated through a parallel tempering simulations at low temperatures, deep in the spin glass phase). After equilibrating the sample, an external field is switched on, and the subsequent dynamics is studied. The field turns out to reduce the relaxation time, but huge statistical fluctuations are found when different samples are compared. After taking care of these fluctuations we find that the expected linear regime is very narrow. Nevertheless, when regarded as a purely numerical method, we find that the external field is extremely effective in reducing the relaxation times., Unión Europea. H2020, Ministerio de Economía y Competitividad (MINECO)/FEDER, Junta de Extremadura/FEDER, Depto. de Física Teórica, Fac. de Ciencias Físicas, TRUE, pub