Spin-glass (SG) states of the 3-dimensional Ising Edwards-Anderson model under a static magnetic field
h are examined by means of the standard Monte Carlo simulation on the field-shift aging protocol at temperature
T. For each process with $(T; \tw, h)$, $\tw$ being the waiting time before the field is switched on, we extract the dynamical crossover time, $\tcr(T; \tw, h)$. We have found a nice scaling relation between the two characteristic length scales which are properly determined from $\tcr$ and $\tw$ and then are normalized by the static field crossover length introduced in the SG droplet theory. This scaling behavior implies the instability of the SG phase in the equilibrium limit even under an infinitesimal
h. In comparison with this numerical result the field effect on real spin glasses is also discussed.
Aging of two-dimensional (2D) Ising spin glasses with short-range interactions
Rb2${\mathrm{Cu}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$
CoxF4 (
Tc=0) is studied in the critical regime via the low-frequency ac susceptibility and via the dc magnetization for x=0.22 and 0.33. After quenching to low temperatures, slow logarithmic relaxation is observed for both the in-phase and out-of-phase ac susceptibilities. Using the droplet scaling model, the spin-glass correlation length R is concluded to increase after a temperature quench as R\ensuremath{\propto}(lnt${)}^{1/\mathrm{\ensuremath{\psi}}}$, with t in units of some microscopic time. The exponent \ensuremath{\psi}=1.0\ifmmode\pm\else\textpm\fi{}0.1 compares with recent theoretical results and numerical simulations for 2D short-range Ising spin glasses. The waiting-time dependence found for the field-cooled and zero-field-cooled dc magnetizations points to a markedly slower crossover from the quasiequilibrium to the nonequilibrium regime than in 3D. From experiments with different cooling histories, finally, the equilibrium spin-glass state is inferred to be strongly dependent on the temperature.
The crossover between quasiequilibrium and nonequilibrium spin-glass dynamics has been studied in Monte Carlo simulations of two- and three-dimensional short-range Ising spin-glass systems. The spin system was quenched in zero field to a low temperature T. After equilibrating for a time
tw, a weak magnetic field was applied and the time dependence of the magnetization M(t) and the spin autocorrelation function q(t) was studied. Our results show that the relaxation rate S(t)=\ensuremath{\partial}M(t)/\ensuremath{\partial}
log10(t) exhibits a maximum at t\ensuremath{\approxeq}
tw. If the temperature is lowered or raised, immediately prior to the field application, the apparent age (
ta) of the system, as defined by the maximum in relaxation rate, is shifted to longer or shorter time scales, respectively. No significant differences between the aging behavior in two and three dimensions are found. The relation \ensuremath{\chi}(t)=[1-q(t)]/T holds only for short time scales (t\ensuremath{\ll}
tw), clear deviations are found at longer time scales (t>
tw). Since this relation should according to the fluctuation-dissipation theorem hold for a system in equilibrium, this result is interpreted as an indication of a crossover between equilibrium and nonequilibrium dynamics. Our results are qualitatively in agreement with experiments as well as with theoretical models for the nonequilibrium spin-glass dynamics.
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.
By means of Monte Carlo simulations on the three-dimensional Ising spin-glass model, we have studied aging phenomena with various temperature(
T)-change protocols. Particularly, a
T-shift protocol, in which a system is first quenched to and aged for a period
tw1 at a temperature
T1, and subsequently aged at a new temperature
T2 is closely investigated. Most importantly, the mean size of domains, which is extracted from the replica-overlap function, was found to grow monotonically without any appreciable decrease by the
T-change. We also found the relaxation of energy density and spin auto-correlation function during the
T-shift process can be explained within the following picture: the dynamics finally crossovers to an isothermal aging of
T2 at around
t2≃tw1(eff) after the
T-change, where
tw1(eff) is an effective waiting time related with
tw1, but in the transient regime
t2<tw1(eff), adjustment of the population of thermally active droplets from that at
T1 to
T2 takes place very slowly. Implications of the results on aging phenomena in other
T-change protocols such as
T-cycling and continuous
T-change with an intermittent stop observed by simulations as well as experiments are discussed.
Growth of the zero-field-cooled magnetization (ZFCM) under continuous heating with and without an intermittent stop(s) is studied on Ising spin glasses both experimentally and numerically. Despite the large difference between time scales of the experiment and the simulation, the ZFCM behavior observed in the two systems can be quantitatively interpreted by means of a common set of the scaling expressions based on the droplet picture. The results strongly suggest that the spin-glass coherence length reached by the laboratory time scales is about a hundred lattice spacings or less. Within this length scale no signature of the chaos effect (rejuvenation) has been found in the ZFCM measured.