arXiv subjects

R. L. Orbach

Publications and source records attributed to R. L. Orbach.

8 recordsLinked to original sources

arXiv2025

Spin-glass dynamics: experiment, theory and simulation

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.

cond-mat.dis-nn↗

arXiv2025

Interplay between aging and rejuvenation in spin glasses

Aging in a single crystal spin glass ($\mathrm{Cu}_{0.92}\mathrm{Mn}_{0.08}$) has been measured using ac susceptibility techniques over a temperature range of $0.3 - 0.8 \, T_g$. In these studies, traditional aging experiments (or ``quench'' aging protocols) are compared to aging curves constructed from finite-cooling-rate curves. By comparing the growth rates of spin glass order between the two types of aging curves, it is determined that quantitative comparisons between protocols which are taken by quenching and protocols using a finite cooling rate are not possible without a deeper understanding of the interplay between aging and rejuvenation. We then demonstrate that the data presented indicate that rejuvenation, rather than cumulative aging, is the cause for the discrepancies between the two growth rates.

cond-mat.dis-nn↗

arXiv2025

Quantifying memory in spin glasses

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.

cond-mat.dis-nn↗

arXiv2024

Memory and Rejuvenation in Glassy Systems

The memory effect in a single crystal spin glass ($\mathrm{Cu}_{0.92}\mathrm{Mn}_{0.08}$) has been measured using \freq ac susceptibility techniques over a temperature range of $0.4 - 0.7 \, T_g$ and a model of the memory effect has been developed. A double-waiting-time protocol is carried out where the spin glass is first allowed to age at a temperature below $T_g$, followed by a second aging at a lower temperature, \Tw{2}, after it has fully rejuvenated. The model is based on calculating typical coincident growth of correlated regions at the two temperatures. It accounts for the absolute magnitude of the memory effect as a function of both waiting times and temperatures. The data can be explained by the memory loss being a function of the relative change in the correlated volume at the first waiting temperature because of the growth in the correlations at the second waiting temperature.

cond-mat.dis-nn↗

arXiv2023

On the superposition principle and non-linear response in spin glasses

The extended principle of superposition has been a touchstone of spin glass dynamics for almost thirty years. The Uppsala group has demonstrated its validity for the metallic spin glass, CuMn, for magnetic fields $H$ up to 10 Oe at the reduced temperature $T_\mathrm{r}=T/T_\mathrm{g} = 0.95$, where $T_\mathrm{g}$ is the spin glass condensation temperature. For $H > 10$ Oe, they observe a departure from linear response which they ascribe to the development of non-linear dynamics. The thrust of this paper is to develop a microscopic origin for this behavior by focusing on the time development of the spin glass correlation length, $ξ(t,t_\mathrm{w};H)$. Here, $t$ is the time after $H$ changes, and $t_\mathrm{w}$ is the time from the quench for $T>T_\mathrm{g}$ to the working temperature $T$ until $H$ changes. We connect the growth of $ξ(t,t_\mathrm{w};H)$ to the barrier heights $Δ(t_\mathrm{w})$ that set the dynamics. The effect of $H$ on the magnitude of $Δ(t_\mathrm{w})$ is responsible for affecting differently the two dynamical protocols associated with turning $H$ off (TRM, or thermoremanent magnetization) or on (ZFC, or zero field-cooled magnetization). In this paper, we display the difference between the zero-field cooled $ξ_{\text {ZFC}}(t,t_\mathrm{w};H)$ and the thermoremanent magnetization $ξ_{\text {TRM}}(t,t_\mathrm{w};H)$ correlation lengths as $H$ increases, both experimentally and through numerical simulations, corresponding to the violation of the extended principle of superposition in line with the finding of the Uppsala Group.

cond-mat.dis-nn↗

arXiv2021

Spin-glass dynamics in the presence of a magnetic field: exploration of microscopic properties

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 $T_\mathrm{g}$. The spin-glass correlation length, $ξ(t,t_\mathrm{w};T)$, is analysed both in experiments and in simulations in terms of the waiting time $t_\mathrm{w}$ after the spin glass has been cooled down to a stabilised measuring temperature $T<T_\mathrm{g}$ 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 $ξ(t,t_\mathrm{w};T)$ 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, $M_\mathrm{ZFC}(t,t_\mathrm{w};T)$, 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.

cond-mat.dis-nn↗

arXiv2020

Scaling law describes the spin-glass response in theory, experiments and simulations

The correlation length $ξ$, 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.

cond-mat.stat-mech↗

arXiv2020

On the Slowing Down of Spin Glass Correlation Length Growth:simulations meet experiments

The growth of the spin-glass correlation length has been measured as a function of the waiting time $t_{\mathrm{w}}$ on a single crystal of CuMn (6 at.\%), reaching values $ξ\sim 150$ nm, larger than any other glassy correlation-length measured to date. We find an aging rate $\mathrm{d}\ln\,t_{\mathrm{w}}/\mathrm{d}\ln\,ξ$ larger than found in previous measurements, which evinces a dynamic slowing-down as $ξ$ grows. Our measured aging rate is compared with simulation results by the Janus collaboration. After critical effects are taken into account, we find excellent agreement with the Janus data.

cond-mat.dis-nn↗