  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=
(d_f + theta)/d_m, where d_f,d_m 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.
