“Avalanches” in the ground state of the 3D Gaussian random field Ising model driven by an external field Original Research Article

We present a numerical study of the exact ground states of the 3D Gaussian random field Ising model (G-RFIM) with an applied external field B. We combine a max-flow min-cut algorithm with an optimal procedure for determining all the ground states when B is swept from −∞ to ∞. The magnetization of finite lattices (L3) is studied as a function of the degree of disorder in the system σ (standard deviation of the Gaussian random fields). The magnetization evolves as a sequence of jumps or “avalanches” with a certain size s. The statistical distribution p(s) becomes a power law p(s)∼s−τ for a certain degree of disorder σc(L). The extrapolation of the results to L→∞ renders σc≃2.4±0.1 and τ≃1.70±0.07.