Analysis of coarsening and aging in Ising spin glasses using record dynamics

Record Dynamics (RD) describes the ubiquitous relaxation phenomenology known as "aging" that ensues after a hard quench in terms of a log-Poisson process. According to RD, a nonequilibrium system after a quench relies on fluctuations that randomly generate a sequence of irreversible record-sized events (quakes or avalanches) that allow the system to escape ever-higher barriers of meta-stable states within a complex energy landscape. Only the activation over such barriers allows the system to relax while tumbling into the next meta-basin that is marginally more stable. Within this picture of RD, a clear distinction can be drawn between the coarsening dynamics of, say, an Ising ferromagnet and the aging of the spin glass, which are often put in the same category. To that end, we use Ising spin models that interpolate between the spin glass and ferromagnet by varying the admixture of anti-ferromagnetic bonds from 50% to zero. Indeed, the accumulation of record events grows logarithmically with time in the glassy regime, with a sharp transition at a specific admixture in the ferromagnetic regime where such activations saturate quickly. We show this effect both for the Edwards-Anderson model on a cubic lattice as well as the Sherrington-Kirkpatrick (mean-field) spin glass.