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arXiv:cond-mat/0312327 · Physical Review B

Aging dynamics of the Heisenberg spin glass

Ludovic Berthier, A. P. Young

Published May 28, 2004• 52 citations
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Abstract

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.

DOI
10.1103/physrevb.69.184423

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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 critical behavior of the gauge-glass and the XYXYXY spin-glass models in three dimensions is studied by analyzing their nonequilibrium aging dynamics. A new numerical method, which relies on the calculation of the two-time correlation and integrated response functions, is used to determine both the critical temperature and the nonequilibrium scaling exponents, both for spin and chiral degrees of freedom. First, the ferromagnetic XYXYXY model is studied to validate this nonequilibirum aging method (NAM) since for this nondisordered system we can compare with known results obtained with standard equilibrium and nonequilibrium techniques. When applied to the case of the gauge-glass model, we show that the NAM allows us to obtain precise and reliable values of its critical quantities, improving previous estimates. The XYXYXY spin-glass model with both Gaussian and bimodal bond distributions is analyzed in more detail. The spin and the chiral two-time correlation and integrated response functions are calculated in our simulations. The results obtained mainly for Gaussian and, to a lesser extent, for bimodal interactions support the existence of a spin-chiral decoupling scenario, where the chiral order occurs at a finite temperature while the spin degrees of freedom order at very low or zero temperature.
Up to now the chirality is seldom studied in the diluted spin glass although many investigations have been performed on the site-ordered Edwards—Anderson model. By simulation, we investigate the dynamical properties of both the spin-glass and the chiral-glass phases in a diluted dipolar system, which was manifested to have a spin-glass transition by recent numerical study. By scaling we find that both phases have the same aging behavior and closer aging parameter μ. Similarly, the domains grow in the same way and both phases have a closer barrier exponent Ψ. It means that both the spins and the chirality have the same dynamical properties and they may freeze at the same temperature.
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.
Spin-glass and chiral-glass orderings of a three-dimensional isotropic Heisenberg spin glass are studied both by equilibrium and off-equilibrium Monte Carlo simulations with emphasis on their dynamical aspects. The model is found to exhibit a finite-temperature chiral-glass transition without the conventional spin-glass order. Although chirality is an Ising-like quantity from symmetry, universality class of the chiral-glass transition appears to be different from that of the standard Ising spin glass. In the off-equilibrium simulation, while the spin autocorrelation exhibits only an interrupted aging, the chirality autocorrelation persists to exhibit a pronounced aging effect reminiscent of the one observered in the mean-field model.
The aging phenomena in Ising spin glasses in a magnetic field are investigated both by the numerical simulation on three-dimensional Ising Edwards-Anderson model and by the experiment on the Fe0.55Mn0.45TiO3 Ising spin glass. After reviewing our recent numerical work on the field-shift aging protocol, by which we argue that the spin-glass (SG) phase is unstable in a static magnetic field of any strength, we present the nonequilibrium aspects of the field-cooled magnetization in a relatively small field observed numerically and experimentally. The results are compatible with the absence of the equilibrium SG phase in a field.
Spin-glass and chiral-glass orderings in three-dimensional Heisenberg spin glasses are studied with and without random magnetic anisotropy by dynamical Monte Carlo simulations. In the isotropic case, clear evidence of a finite-temperature chiral-glass transition is presented. While the spin autocorrelation exhibits only an interrupted aging, the chirality autocorrelation persists to exhibit a pronounced aging effect reminiscent of the one observed in the mean-field model. In the anisotropic case, asymptotic mixing of the spin and the chirality is observed in the off-equilibrium dynamics.