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arXiv:cond-mat/0303406 · Physical Review Letters

Temperature Chaos, Rejuvenation, and Memory in Migdal-Kadanoff Spin Glasses

M. Sasaki, Olivier Martin

Published Aug 27, 2003• 27 citations
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Abstract

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.

DOI
10.1103/physrevlett.91.097201

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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.
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 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.
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 argue that the chaotic temperature effect predicted in Ising spin glasses should be stronger when one considers continuous ( XY , Heisenberg) kind of spins, due to bigger entropic fluctuations. We then discuss the behavior of 3d spin glasses using the Migdal-Kadanoff Renormalization Group for Ising and XY spins, where we show explicitly that the chaotic length scale, the length beyond which equilibrium configurations are completly reshuffled when one changes temperature, could be far smaller for XY than for Ising spins. These results could thus explain why experiments are seeing a stronger rejuvenation effect for continuous spins.
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.