Finite Size Scaling analysis of the avalanches in the 3d Gaussian Random   Field Ising Model with metastable dynamics
  A numerical study is presented of the 3d Gaussian Random Field Ising Model at T=0 driven by an external field. Standard synchronous relaxation dynamics is employed to obtain the magnetization versus field hysteresis loops. The focus is on the analysis of the number and size distribution of the magnetization avalanches. They are classified as being non-spanning, 1d-spanning, 2d-spanning or 3d-spanning depending on whether or not they span the whole lattice in the different space directions. Moreover, finite-size scaling analysis enables identification of two different types of non-spanning avalanches (critical and supercritical) and two different types of 3d-spanning avalanches (critical and subcritical), whose numbers increase with L as a power-law with different exponents. We conclude by giving a scenario for the avalanches behaviour in the thermodynamic limit. 
F.J.Perez-Reche and Eduard Vives