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.
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.
We study the nonequilibrium aging behavior of the $\ifmmode\pm\else\textpm\fi{}J$ Edwards-Anderson model in three dimensions for samples of size up to
N=1283 and for up to
108 Monte Carlo sweeps. In particular we are interested in the change of the aging when crossing from the spin-glass phase to the ferromagnetic phase. The necessary long simulation times are reached by employing a CUDA-based GPU implementation, which allows for single-spin flip times as small as 8 ps. We measure typical spin-glass correlation functions in space and time to determine the growing length scale and extract the constituting exponents. We observe a clear signature of the disorder-driven equilibrium transition in the nonequilibrium behavior.
The deviations from full or pure aging behavior, i.e. perfect
t/tw scaling of the correlation and response functions of aging glassy systems, are not well understood theoretically. Recent experiments of Rodriguez et al. (Phys. Rev. Lett. 91, 037203 (2003)) have shown that full aging applies to the thermoremanent magnetization in the limit of infinite cooling rate during the initial quench. In numerical models, instantaneous thermal quenches can be--and usually are--applied. This has motivated the present numerical investigations of the aging behavior of Edwards-Anderson Ising spin glass models with both short- and long-range Gaussian interactions, respectively. We sample the distribution of residence time
t in suitably defined metastable valleys entered at age
tw, finding that the deviations from
t/tw scaling are small and decrease systematically as the system size grows and/or the temperature decreases. Finally, the connection between this behavior and the scaling of the correlation function itself is discussed.
As an analysis of equilibrium phase transitions, the nonequilibrium relaxation method is extended to the spin glass (SG) transition. The $\ifmmode\pm\else\textpm\fi{}J$ Ising SG model is analyzed for three-dimensional (cubic) lattices up to the linear size of
L=127 and for four-dimensional (hypercubic) lattice up to
L=41. These sizes of systems are quite large as compared with those calculated, so far, by equilibrium simulations. As a dynamical order parameter, we calculate the clone correlation function (CCF) ${Q(t,t}_{\mathrm{w}})\ensuremath{\equiv}[〈{S}_{i}^{(1)}{(t+t}_{\mathrm{w}}){S}_{i}^{(2)}{(t+t}_{\mathrm{w}}){〉}^{\mathrm{F}}],$ which is a spin correlation of two replicas produced after the waiting time
tw from a simple starting state. It is found that the CCF shows an exponential decay in the paramagnetic phase, and a power-law decay after aginglike development $(t\ensuremath{\gg}{t}_{\mathrm{w}})$ in the SG phase. This provides a reliable upper bound of the transition temperature
Tg. It is also found that a scaling relation, ${Q(t,t}_{\mathrm{w}}{)=t}_{\mathrm{w}}^{\ensuremath{-}{\ensuremath{\lambda}}_{q}}\overline{q}{(t/t}_{\mathrm{w}}),$ holds just around the transition point providing the lower bound of
Tg. Together with these two bounds, we propose a new dynamical way for the estimation of
Tg from much larger systems. In the SG phase, the power-law behavior of the CCF for $t\ensuremath{\gg}{t}_{\mathrm{w}}$ suggests that the SG phase in short-range Ising models has a rugged phase space.