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.
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.
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.
Aging phenomena of short-range Ising spin glass models have been investigated using Monte Carlo simulations. It is found that in the low-temperature spin-glass phase the mean domain size exhibits a crossover from a power-law growth associated with the critical fluctuation at the transition temperature to slower growth inherent in the low-temperature phase. The temperature dependence of the growth law of the domain size can be almost explained by this crossover. We also find that the spin-autocorrelation function in the quasi-equilibrium regime follows the expected scaling behavior from the droplet theory expressed in terms of the mean domain size and a characteristic length scale of droplet excitations. Spin glasses (SG) exhibit characteristic slow dynamics below the SG transition temperature. 1)-3) Recently such slow dynamics, in particular aging phenomena, has been much attractive both in experimental and theoretical studies. Several attempts have been made so far to explain the slow dynamics. There are mainly two distinct
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 such that length scales smaller than
lT are equilibrated, whereas larger length scales are essentially frozen. The time and temperature dependences of
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.
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.