Abstract
We present a formalism for computing the complexity of metastable states and thezero-temperature magnetic hysteresis loop in the soft-spin random-field model in finitedimensions. The complexity is obtained as the Legendre transform of the free energyassociated with a certain action in replica space and the hysteresis loop above thecritical disorder is defined as the curve in the field–magnetization plane where thecomplexity vanishes; the nonequilibrium magnetization is therefore obtained withouthaving to follow the dynamical evolution. We use approximations borrowed fromcondensed-matter theory and based on assumptions on the structure of the directcorrelation functions (or proper vertices), such as a local approximation for theself-energies, to calculate the hysteresis loop in three dimensions, the correlationfunctions along the loop, and the second moment of the avalanche-size distribution.
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