Monte Carlo studies of Ising spin-glass systems: Aging behavior and crossover between equilibrium and nonequilibrium dynamics

Experimental evidence for violation of the fluctuation-dissipation theorem in a superspin glass

We present the experimental observation of the fluctuation-dissipation theorem violation in an assembly of interacting magnetic nanoparticles in the low temperature superspin-glass phase. The magnetic noise is measured with a two-dimension electron gas Hall probe and compared to the out of phase ac susceptibility of the same ferrofluid. For "intermediate" aging times of the order of 1 h, the ratio of the effective temperature T(eff) to the bath temperature T grows from 1 to 6.5 when T is lowered from T(g) to 0.3 T(g), regardless of the noise frequency. These values are comparable to those measured in an atomic spin glass as well as those calculated for a Heisenberg spin glass.

Thermal shifts and intermittent linear response of aging systems

At time t after an initial quench, an aging system responds to a perturbation turned on at time tw<t in a way mainly depending on the number of intermittent energy fluctuations, so-called quakes, which fall within the observation interval (tw,t] [P. Sibani, G. F. Rodriguez, and G. G. Kenning, Phys. Rev. B 74, 224407 (2006); P. Sibani, Eur. J. Phys. B 58, 483 (2007)]. The temporal distribution of the quakes implies a functional dependence of the average response on the ratio t/tw . Further insight is obtained imposing small temperature steps, so-called T shifts. The average response as a function of t/tw,eff , where tw,eff is the effective age, is similar to the response of a system aged isothermally at the final temperature. Using an Ising model with plaquette interactions, the applicability of analytic formulas for the average isothermal magnetization is confirmed. The T -shifted aging behavior of the model is approximately described using effective ages. Large positive shifts nearly reset the effective age. Negative T shifts offer a more detailed probe of the dynamics. Assuming the marginal stability of the "current" attractor against thermal noise fluctuations, the scaling form tw,eff=tw x and the dependence of the exponent x on the aging temperatures before and after the shift are theoretically available. The predicted form of x has no adjustable parameters. Both the algebraic scaling of the effective age and the form of the exponent reasonably agree with the data. The present simulations thus confirm the crucial role of marginal stability in glassy relaxation.

Aging and self-organized criticality in driven dissipative systems

We study the noisy dynamics of a close relative to the original sandpile model. Depending on the type of noise and the time scale of observation, we find stationary fluctuations (similar to self-organized criticality) or an aging dynamics with punctuated equilibria, a decreasing rate of events and reset properties qualitatively similar to those of glassy systems, evolution models, and vibrated granular media.

Dynamic ultrametricity in spin glasses

We investigate the dynamics of spin glasses from the "rheological" point of view, in which aging is suppressed by the action of small, nonconservative forces. The different features can be expressed in terms of the scaling of relaxation times with the magnitude of the driving force, which plays the role of the critical parameter. Stated in these terms, ultrametricity loses much of its mystery and can be checked rather easily. This approach also seems a natural starting point to investigate what would be the real-space structures underlying the hierarchy of time scales. We study in detail the appearance of this many-scale behavior in a mean-field model, in which dynamic ultrametricity is clearly present. A similar analysis is performed on numerical results obtained for a three-dimensional spin glass: In that case, our results are compatible with either that dynamic ultrametricity is absent or that it develops so slowly that even in experimental time-windows it is still hardly observable.

Off-equilibrium dynamics of the frustrated Ising lattice gas

We study by means of Monte Carlo simulations the off-equilibrium properties of a model glass, the frustrated Ising lattice gas in three dimensions. We have computed typical two times quantities, such as density-density autocorrelations and the autocorrelation of internal degrees of freedom. We find an aging scenario particularly interesting in the case of the density autocorrelations in real space that is very reminiscent of spin glass phenomenology. While this model captures the essential features of structural glass dynamics, its analogy with spin glasses may make possible its complete description using the tools developed in spin glass theory.