Anisotropic Scaling of Avalanches in the Random Field Ising Model

Joel Clemmer*, Mark Robbins, Department of Physics and Astronomy, Johns Hopkins University


“Driven interfaces in a wide variety of systems undergo a critical depinning transition as the driving force is increased to a critical value. Near this transition, growth consists of discrete avalanches with a power law distribution of sizes and a diverging correlation length along the interface.

We simulate the depinning of a self-affine domain wall in the 3D random field Ising model to determine the how the height of an avalanche scales relative to its width. Scaling theories often assume that avalanches are isotropic or their anisotropy is described by the roughness exponent α = 2/3. Our analysis shows the height of an avalanche grows sublinearly with the width, characterized by an new exponent of 0.85.

Due to the small deviation from the predicted scalings of 2/3 or 1.0, isolating this exponent required recent advances in computing. The largest systems studied consist of >1012 spins and require >4TB of RAM to run.”