Nonequilibrium dynamics of spin glasses

We consider the nonequilibrium behavior of the spin-glass ordered phase within the droplet scaling theory introduced previously. The fundamental long-time nonequilibrium process is assumed to be the thermally activated growth of spin-glass ordered domains. The remanent magnetization, m(t), in zero field is found to decay at long times as m(t)∼$R_t^{\mathrm{-}\lambda }$, where $R_t$∼(lnt${)}^{1/\psi }$ is the linear domain size, ψ is the previously introduced barrier exponent describing the growth of activation-barrier heights with length scale, and λ is a new nonequilibrium dynamic exponent, satisfying the relation λ≥d/2 for d-dimensional systems. The effects of waiting for partial equilibration before making a measurement are studied in various regimes. The effects of quenching first to one temperature and then to another are also examined. Such experiments can, in principle, be used to obtain information about the relative rate of dynamic evolution as well as the overlap between the equilibrium states at different temperatures. In particular, the length scale $L_{\Delta T}$, below which equilibrium correlations at temperatures T and T+ΔT are similar, plays an important role. The decay of m(t) and the growth of spin-glass order after a quench are examined in Monte Carlo simulations of the Sherrington-Kirkpatrick model.