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arXiv:cond-mat/0106539 · Physical review. B, Condensed matter

Separation of time and length scales in spin glasses: Temperature as a microscope

Jean‐Philippe Bouchaud, Vincent Dupuis, J. Hammann, E. Vincent

Published Dec 19, 2001• 138 citations
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Abstract

We summarize the different puzzles raised by aging experiments of spin glasses and their various interpretations. We try to reconcile the ``real space,'' dropletlike pictures with the hierarchical pictures that have been proposed in the past. The basic ingredient is a strong separation of the time scales that govern the dynamics of the system on different length scales. Changing the temperature abruptly changes the length scale at which the system is observed, thereby allowing rejuvenation (that concerns short length scales) and memory (stored in long length scales) to coexist. We show that previous experiments can be reanalyzed in terms of vanishing free-energy barriers at the spin-glass transition, an important ingredient to obtain a fast separation of time scales. We propose to distinguish between ``fixed landscape rejuvenation,'' which is already present in simple two (or multi) level systems, from the ``strong'' chaos effect on scales larger than the ``overlap length'' conjectured in the context of the droplet model. We argue that most experiments can be accounted for without invoking the existence of an overlap length. Experiments are presented to test some recent predictions of the strong chaos scenario, with negative results.

DOI
10.1103/physrevb.65.024439

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We summarize the different puzzles raised by aging experiments of spin glasses and their various interpretations. We try to reconcile the real space,'' dropletlike pictures with the hierarchical pictures that have been proposed in the past. The basic ingredient is a strong separation of the time scales that govern the dynamics of the system on different length scales. Changing the temperature abruptly changes the length scale at which the system is observed, thereby allowing rejuvenation (that concerns short length scales) and memory (stored in long length scales) to coexist. We show that previous experiments can be reanalyzed in terms of vanishing free-energy barriers at the spin-glass transition, an important ingredient to obtain a fast separation of time scales. We propose to distinguish between fixed landscape rejuvenation,'' which is already present in simple two (or multi) level systems, from the strong'' chaos effect on scales larger than the overlap length'' conjectured in the context of the droplet model. We argue that most experiments can be accounted for without invoking the existence of an overlap length. Experiments are presented to test some recent predictions of the strong chaos scenario, with negative results.
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.
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.
We present a comprehensive study of nonequilibrium phenomena in the low-temperature phase of the Edwards-Anderson Gaussian spin glass in three and four spatial dimensions. Many effects can be understood in terms of a time-dependent coherence length lT{l}_{T}lT​ such that length scales smaller than lT{l}_{T}lT​ are equilibrated, whereas larger length scales are essentially frozen. The time and temperature dependences of lT{l}_{T}lT​ are found to be compatible with critical power-law dynamical scaling for small times and high temperatures, crossing over to an activated logarithmic growth for longer times and lower temperatures, in agreement with recent experimental results. The activated regime is governed by a ``barrier exponent'' $\ensuremath{\psi}$ which we estimate to be $\ensuremath{\psi}\ensuremath{\sim}1.0$ and 2.3 in three and four dimensions, respectively. We observe the rejuvenation and memory effects in the four-dimensional sample, which, we argue, is unrelated to ``temperature chaos.'' Our discussion in terms of length scales allows us to address several experimentally relevant issues, such as superaging versus subaging effects, the role of a finite cooling rate, or the so-called Kovacs effect.
We use simulations within the Migdal-Kadanoff approach to probe the scales relevant for rejuvenation and memory in Ising spin glasses. First we investigate scaling laws for domain wall free energies and extract the chaos overlap length l(T,T'). Then we perform out of equilibrium simulations that follow experimental protocols. We find that (1) a rejuvenation signal arises at a length scale significantly smaller than l(T,T'), and (2) memory survives even if equilibration goes out to length scales larger than l(T,T'). Theoretical justifications of these phenomena are then considered.
The slow nonequilibrium dynamics of the Edwards-Anderson spin-glass model on a hierarchical lattice is studied by means of a coarse-grained description based on renormalization concepts. We evaluate the isothermal aging properties and show how the occurrence of temperature chaos is connected to a gradual loss of memory when approaching the overlap length. This leads to rejuvenation effects in temperature shift protocols and to rejuvenation-memory effects in temperature cycling procedures with a pattern of behavior parallel to experimental observations.
We numerically study aging for the Edwards-Anderson model in three and four dimensions using different temperature-change protocols. In D=3D=3D=3, time scales a thousand times larger than in previous work are reached with the Spin Update Engine (SUE) machine. Deviations from cumulative aging are observed in the nonmonotonic time behavior of the coherence length. Memory and rejuvenation effects are found in a temperature-cycle protocol, revealed by vanishing effective waiting times. Similar effects are reported for the D=3D=3D=3 site-diluted ferromagnetic Ising model (without chaos). However, rejuvenation is reduced if off-equilibrium corrections to the fluctuation-dissipation theorem are considered. Memory and rejuvenation are quantitatively describable in terms of the growth regime of the spin-glass coherence length.