Equilibrium avalanches in spin glasses

Original · EN

We study the distribution of equilibrium avalanches (shocks) in Ising spin glasses which occur at zero temperature upon small changes in the magnetic field. For the infinite-range Sherrington-Kirkpatrick model we present a detailed derivation of the density rho(Delta M) of the magnetization jumps Delta M. It is obtained by introducing a multi-component generalization of the Parisi-Duplantier equation, which allows us to compute all cumulants of the magnetization. We find that rho(Delta M) (Delta M)(-tau) with an avalanche exponent tau=1 for the SK model, originating from the marginal stability (criticality) of the model. It holds for jumps of size 1 << Delta M < N(1/2) being provoked by changes of the external field by delta H = O(N[-1/2]) where N is the total number of spins. Our general formula also suggests that the density of overlap q between initial and final state in an avalanche is rho(q) 1/(1-q). These results show interesting similarities with numerical simulations for the out-of-equilibrium dynamics of the SK model. For finite-range models, using droplet arguments, we obtain the prediction tau= (df + theta)/dₘ, where df,dₘ and theta are the fractal dimension, magnetization exponent and energy exponent of a droplet, respectively. This formula is expected to apply to other glassy disordered systems, such as the random-field model and pinned interfaces. We make suggestions for further numerical investigations, as well as experimental studies of the Barkhausen noise in spin glasses.