Studying avalanches in the ground state of the two-dimensional random-field Ising model driven by an external field

We study the exact ground state of the two-dimensional random-field Ising m odel as a function of both the external applied field B and the standard de viation sigma of the Gaussian random-field distribution. The equilibrium ev olution of the magnetization consists in a sequence of discrete jumps. Thes e are very similar to the avalanche behavior found in the out-of-equilibriu m version of the same model with local relaxation dynamics. We compare the statistical distributions of magnetization jump!: and find that both exhibi t power-law behavior for the same value of sigma. The corresponding exponen ts are compared.