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arXiv:2307.02224 · Physical Review Letters

Quantifying Memory in Spin Glasses

Ilaria Paga, J. P. He, Marco Baity‐Jesi, Enrico Calore, Andrés De la Cruz, L. A. Fernández, Jose Miguel Gil-Narvion, I. González-Adalid Pemartín, A. Gordillo-Guerrero, D. Íñiguez, A. Maiorano, Enzo Marinari, Víctor Martín-Mayor, J. Moreno-Gordo, A. Muñoz Sudupe, Denis Navarro, R. Orbach, Giorgio Parisi A, Sergio Perez-Gaviro, Federico Ricci‐Tersenghi, Juan Jesus Ruiz-Lorenzo, Sebastiano Fabio Schifano, Deborah L. Schlagel, Beatriz Seoane, Alfonso Tarancón, David Yllanes

Published Dec 20, 2024• 5 citations
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Abstract

Rejuvenation and memory, long considered the distinguishing features of spin glasses, have recently been proven to result from the growth of multiple length scales. This insight, enabled by simulations on the Janus II supercomputer, has opened the door to a quantitative analysis. We combine numerical simulations with comparable experiments to introduce two coefficients that quantify memory. A third coefficient has been recently presented by Freedberg et al. We show that these coefficients are physically equivalent by studying their temperature and waiting-time dependence.

DOI
10.1103/physrevlett.133.256704

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Rejuvenation and memory, long considered the distinguishing features of spin glasses, have recently been proven to result from the growth of multiple length scales. This insight, enabled by simulations on the Janus II supercomputer, has opened the door to a quantitative analysis. We combine numerical simulations with comparable experiments to introduce two coefficients that quantify memory. A third coefficient has been recently presented by Freedberg et al. We show that these coefficients are physically equivalent by studying their temperature and waiting-time dependence.
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 (maybe the most exotic features in glassy free-energy landscapes). 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 simulate reliably. Yet, three recent developments convinced us to accept this challenge: first, the custom-built Janus II supercomputer makes it possible to carry out "numerical experiments" in which the very same quantities that can be measured in single crystals of CuMn are computed from the simulation, allowing for parallel analysis of the simulation/experiment 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 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, while essentially all theoretical analyses of the aging dynamics emphasize the presence and the crucial role of a single glassy correlation length.
Experiments on spin glasses can now make precise measurements of the exponent z(T) governing the growth of glassy domains, while our computational capabilities allow us to make quantitative predictions for experimental scales. However, experimental and numerical values for z(T) have differed. We use new simulations on the Janus II computer to resolve this discrepancy, finding a time-dependent z(T,t_{w}), which leads to the experimental value through mild extrapolations. Furthermore, theoretical insight is gained by studying a crossover between the T=T_{c} and T=0 fixed points.
We study aging phenomena of Migdal-Kadanoff spin glasses in order to clarify relevancy of temperature chaos to rejuvenation and memory. By exploiting renormalization, we do efficient dynamical simulations in very wide time/length scales including the chaos length. As a consequence, we find that temperature chaos and temperature dependence of speed of equilibration cause two significantly different effects against temperature variations, i.e., rejuvenation for positive temperature variation and memory for negative temperature variation, as are observed experimentally in spin glasses.
Aging phenomena have been studied in very different materials like polymers, supercooled liquids or disordered orientational crystals. We recall here the main features of aging in spin glasses, and use this example of magnetic systems as a guideline for the description of the others. A particular attention is put on the sensitivity of aging to the cooling rate and to temperature variations. This allows us to point out differences between temperature specific processes, yielding ``rejuvenation and memory effects'' as known in spin glasses, and domain growth processes, giving cumulative contributions at different temperatures. The relevance of wall depinning processes to rejuvenation and memory effects is discussed at the light of recent results on disordered ferromagnets.