Equilibrium avalanches in spin glasses
Pierre Le Doussal1, Markus Müller2, Kay Jörg Wiese1
1CNRS-Laboratoire de Physique Théorique de
l'Ecole Normale Supérieure,
24 rue Lhomond, 75005 Paris, France,
2The Abdus Salam International Center for Theoretical Physics, Strada Costiera 11, 34151 Trieste, Italy.
Abstract
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 ρ(ΔM) of the magnetization jumps ΔM. 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 ρ(ΔM) ~ (ΔM)−τ with an avalanche exponent τ = 1 for the SK model, originating from the marginal stability (criticality) of the model. It holds for jumps of size 1 ≪ ΔM < N1/2 being provoked by changes of the external field by δH = 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 ρ(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 τ = (df + θ)/dm, where df, dm and θ 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.
arXiv:1110.2011 [pdf]
Phys. Rev. B 85 (2012) 214402 [pdf]
Copyright (C) by Kay Wiese. Last edited July 14, 2010.