Influence of the aspect ratio and boundary conditions on universal finite size scaling functions in the athermal metastable 2d Random Field Ising Model

摘要

This work studies universal finite size scaling functions for the number of1d spanning avalanches in a two-dimensional disordered system with boundaryconditions of different nature and different aspect ratios. For this purpose,we consider the 2d Random Field Ising Model at T = 0 driven by the externalfield H with athermal dynamics implemented with periodic and forced boundaryconditions. We choose a convenient scaling variable z that accounts for thedeformation of the distance to the critical point caused by the aspect ratio.Moreover, assuming that the dependence of the finite size scaling functions onthe aspect ratio can be accounted by an additional multiplicative factor, wehave been able to collapse data for different system sizes, different aspectratios and different nature of the boundary conditions into a single scalingfunction Q.