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• W2964332008 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 (SK) model, we present a detailed derivation of the density $ensuremath{rho}(ensuremath{Delta}M)$ of the magnetization jumps $ensuremath{Delta}M$. It is obtained by introducing a multicomponent generalization of the Parisi-Duplantier equation, which allows us to compute all cumulants of the magnetization. We find that $ensuremath{rho}(ensuremath{Delta}M)ensuremath{sim}ensuremath{Delta}{M}^{ensuremath{-}ensuremath{tau}}$ with an avalanche exponent $ensuremath{tau}=1$ for the SK model, originating from the marginal stability (criticality) of the model. It holds for jumps of size $1ensuremath{ll}ensuremath{Delta}M<{N}^{1/2}$, being provoked by changes of the external field by $ensuremath{delta}H=O({N}^{ensuremath{-}1/2})$ where $N$ is the total number of spins. Our general formula also suggests that the density of overlap $q$ between initial and final states in an avalanche is $ensuremath{rho}(q)ensuremath{sim}1/(1ensuremath{-}q)$. 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 $ensuremath{tau}=({d}_{mathrm{f}}+ensuremath{theta})/{d}_{mathrm{m}}$ where ${d}_{mathrm{f}},phantom{rule{0.28em}{0ex}}{d}_{mathrm{m}}$, and $ensuremath{theta}$ 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." @default.
• W2964332008 created "2019-07-30" @default.
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• W2964332008 date "2012-06-05" @default.
• W2964332008 modified "2023-10-15" @default.
• W2964332008 title "Equilibrium avalanches in spin glasses" @default.
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• W2964332008 doi "https://doi.org/10.1103/physrevb.85.214402" @default.
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