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arXiv:cond-mat/0503012 · Physical Review B

Temperature cycles in the Heisenberg spin glass

Ludovic Berthier, A. P. Young

Published Jun 30, 2005• 37 citations
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Abstract

We study numerically the nonequilibrium dynamics of the three-dimensional Heisenberg Edwards-Anderson spin glass submitted to protocols during which temperature is shifted or cycled within the spin glass phase. We show that (partial) rejuvenation and (perfect) memory effects can be numerically observed and study both effects in detail. We quantitatively characterize their dependences on parameters such as the amplitude of the temperature changes, the time scale at which the changes are performed, and the cooling rates used to vary the temperature. We contrast our results both to those found numerically in the Ising version of the model, and to experimental results in different samples. We discuss the theoretical interpretations of our findings, arguing, in particular, that ``full'' rejuvenation can be observed in experiments even if temperature chaos is absent.

DOI
10.1103/physrevb.71.214429

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We study numerically the nonequilibrium dynamics of the three-dimensional Heisenberg Edwards-Anderson spin glass submitted to protocols during which temperature is shifted or cycled within the spin glass phase. We show that (partial) rejuvenation and (perfect) memory effects can be numerically observed and study both effects in detail. We quantitatively characterize their dependences on parameters such as the amplitude of the temperature changes, the time scale at which the changes are performed, and the cooling rates used to vary the temperature. We contrast our results both to those found numerically in the Ising version of the model, and to experimental results in different samples. We discuss the theoretical interpretations of our findings, arguing, in particular, that ``full'' rejuvenation can be observed in experiments even if temperature chaos is absent.
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 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.
We numerically study the nonequilibrium dynamics of the three-dimensional Heisenberg Edwards-Anderson spin glass following a sudden quench to its low-temperature phase. The subsequent aging behavior of the system is analyzed in detail, and the scaling behavior of various space-time correlation functions is investigated for both spin and chiral degrees of freedom. We carefully compare our results with those obtained from simulations of the more studied Ising version of the model, and with experiments on real spin glasses in which the spins have vectorial character. Finally, the present dynamical study offers perspectives into the possibility of spin-chirality decoupling at low temperature in vectorial spin glasses.
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 study and discuss rejuvenation and memory (numerical) experiments in Ising and Heisenberg three and four dimensional spin glasses. We introduce a quantitative procedure to analyze the results of temperature cycling experiments. We also run, compare, and discuss ``twin'' couples of experiments. We find that in our systems aging is always cumulative in nature, and rejuvenation and memory effects are also cumulative: they are very different from the ones observed in experiments on spin glass materials.
The temperature (TTT)-shift protcol of aging in the 3 dimensional (3D) Edwards- Anderson (EA) spin-glass (SG) model is studied through the out-of-phase component of the ac susceptibility simulated by the Monte Carlo method. For processes with a small magnitude of the TTT-shift, ΔTΔTΔT, the memory imprinted before the TTT-shift is preserved under the TTT-change and the SG short-range order continuously grows after the TTT-shift, which we call the cumulative memory scenario. For a negative TTT-shift process with a large ΔTΔTΔT the deviation from the cumulative memory scenario has been observed for the first time in the numerical simulation. We attribute the phenomenon to the `chaos effect' which, we argue, is qualitatively different from the so-called rejuvenation effect observed just after the TTT-shift.