  We have measured magnetic-field-induced avalanches in a square artificial
spin ice array of interacting nanomagnets. Starting from the ground state
ordered configuration, we imaged the individual nanomagnet moments after each
successive application of an incrementally increasing field. The statistics of
the evolution of the moment configuration show good agreement with the
canonical one-dimensional random field Ising model. We extract information
about the microscopic structure of the arrays from our macroscopic measurements
of their collective behavior, demonstrating a process that could be applied to
other systems exhibiting avalanches.
