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© 2012 National Academy of Sciences. Artículo firmado por 22 autores. We thank Davide Rossetti for introducing us to the handling of the 128-bit registers. We acknowledge partial financial support from Ministerio de Ciencia e Innovación (MICINN), Spain, (contract nos. FIS2009-12648-C03, FIS2010-16587, TEC2010-19207), from Universidad Complutense de Madrid (UCM)-Banco de Santander (GR32/10-A/910383), from Junta de Extremadura, Spain (contract no. GR10158), and from Universidad de Extremadura (contract no. ACCVII-08). B.S. and D.Y. were supported by the Formación de Profesorado Universitario (FPU) program (Ministerio de Educación, Spain); R.A.B. and J.M.-G. were supported by the Formación de Personal Investigador (FPI) program (Diputación de Aragón, Spain); finally J.M.G.-N. was supported by the FPI program (Ministerio de Ciencia e Innovación, Spain)., Spin glasses are a longstanding model for the sluggish dynamics that appear at the glass transition. However, spin glasses differ from structural glasses in a crucial feature: they enjoy a time reversal symmetry. This symmetry can be broken by applying an external magnetic field, but embarrassingly little is known about the critical behavior of a spin glass in a field. In this context, the space dimension is crucial. Simulations are easier to interpret in a large number of dimensions, but one must work below the upper critical dimension (i.e., in d < 6) in order for results to have relevance for experiments. Here we show conclusive evidence for the presence of a phase transition in a four-dimensional spin glass in a field. Two ingredients were crucial for this achievement: massive numerical simulations were carried out on the Janus special-purpose computer, and a new and powerful finite-size scaling method., Ministerio de Ciencia e Innovación (MICINN), Universidad Complutense de Madrid (UCM)-Banco de Santander, Junta de Extremadura, Spain, Universidad de Extremadura, Spain, Formación de Profesorado Universitario (FPU) program (Ministerio de Educación, Spain), Formación de Personal Investigador (FPI) program (Diputación de Aragón, Spain), FPI program (Ministerio de Ciencia e Innovación, Spain), 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

© 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