Spin-glass dynamics: experiment, theory and simulation

TL;DR

The paper surveys spin-glass dynamics through experiments, theory, and dedicated simulations, focusing on the growth of a glassy coherence length $\xi$ and its role in aging, rejuvenation, and memory. It elucidates how off-equilibrium dynamics relate to equilibrium structures via generalized fluctuation-dissipation relations and a statics-dynamics dictionary, bridging measurements in real materials with EA/SK models and ultrametric pictures. Key contributions include quantitative extraction of $\xi(t,t_w;H)$ from Zeeman energy, refined mappings between experimental and numerical length scales (notably via Janus II), and a unified scaling framework linking memory, temperature chaos, and nonlinear responses across protocols. The review highlights the experimental reach now possible with single crystals and compares it to state-of-the-art simulations, outlining future directions in theory (RG extensions, chiral scenarios), computation (advanced hardware and algorithms), and experiments (long-time thin-film dynamics, chaos onset, and memory phenomena). The work underscores spin glasses as a paradigmatic, highly interdisciplinary system, with implications spanning optimization, neural networks, and complex systems at large, exemplified by the Ising EA and SK models, replica symmetry breaking, and ultrametric organization of metastable states.

Abstract

The study of spin-glass dynamics, long considered the paradigmatic complex system, has reached important milestones. The availability of single crystals has allowed the experimental measurement of spin-glass coherence lengths of almost macroscopic dimensions, while the advent of special-purpose computers enables dynamical simulations that approach experimental scales. This review provides an account of the quantitative convergence of these two avenues of research, with precise experimental measurements of the expected scaling laws and numerical reproduction of classic experimental results, such as memory and rejuvenation. The article opens with a brief review of the defining spin-glass properties, randomness and frustration, and their experimental consequences. These apparently simple characteristics are shown to generate rich and complex physics. Models are introduced that enable quantitative dynamical descriptions. After a summary of the main numerical results in equilibrium, paying particular attention to temperature chaos, this review examines off-equilibrium dynamics in the absence of a magnetic field and shows how it can be related to equilibrium structures through the fluctuation-dissipation relations. The nonlinear response at a given temperature is then developed, including experiments and scaling in the vicinity of the transition temperature $T_\mathrm{g}$. The consequences of temperature change $\unicode{x2013}$including temperature chaos, rejuvenation, and memory$\unicode{x2013}$ are reviewed. The interpretation of these phenomena requires identifying several length scales relevant to dynamics, which, in turn, generate new insights. Finally, issues for future investigations are introduced, including what is to be nailed down theoretically, why the Ising Edwards-Anderson model is so successful at modeling spin-glass dynamics, and experiments yet to be undertaken.

Figures (56)

• Figure 1: Susceptibility for AuFe $1\leq {\text{c}}\leq 8$ at.% in the region of low magnetic fields. The data were taken every $0.25$ K around the peak and every $0.5$ or 1 K elsewhere. The scatter of the points is of the order of the thickness of the lines. The open circles indicate isolated points taken at higher temperatures. Reproduced from Fig. 9 of cannella:72.
• Figure 2: The mean ac spin-glass temperature, $T_\mathrm{g}\xspace$, vs the logarithm of the measuring frequency for different concentrations in AgMn samples. $\blacklozenge$, 5,000 ppm, HF (0.4 to 2.8 MHz); $\Diamond$, 5,000 ppm MF (93 to 109 kHz); $\triangledown$, 3,000 ppm MF (93 to 109 kHz); $\blacktriangledown$, 3,000 ppm LF (16 to 160 Hz); and $\square$, 2,000 ppm MF (93 Hz to 109 kHz). The vertical error bars are equal to two standard deviations of the $T_\mathrm{g}$ measurements at a particular frequency. Reproduced from Fig. 2 of dahlberg:79.
• Figure 3: The absolute variation of $T_\text{f}$ (equivalent to what we call $T_\mathrm{g}$ in this review) per decade of time, reported as a function of $x$, the percentage fraction of Mn, for CuMn ($1\% <x < 10\%$). It can be represented by an $x^{2/3}$ law. Reproduced from Fig. 2 of tholence:81.
• Figure 4: Specific heat of Au$_{0.92}$Fe$_{0.08}$ in the temperature region 3-50 K is shown as a plot of $C/T$ vs $T^2$. The solid curve is the calculated nonmagnetic contribution to the specific heat of the alloy between 0 and 30 K. The inset shows the susceptibility results of the same sample, which were provided by S. A. Werner. Reproduced from Fig. 2 of wenger:75 and wenger:76.
• Figure 5: The field-cooled (FC, upper), zero-field-cooled (ZFC, lower), and thermoremanent (TRM, middle) magnetizations against temperature for CdCr$_{1.7}$In$_{0.3}$$S_4$ in an external magnetic field $H=10$ G. Reproduced from Fig. 1 of vincent:24 and dupuis:02.