This work studies universal finite size scaling functions for the number of one-dimensional spanning avalanches in a two-dimensional (2D) disordered system with boundary conditions of different nature and different aspect ratios. To this end, we will consider the 2D random field Ising model at $T=0$ driven by the external field $H$ with athermal dynamics implemented with periodic and forced boundary conditions. We have chosen a convenient scaling variable $z$ that accounts for the deformation of the distance to the critical point caused by the aspect ratio. In addition, assuming that the dependence of the finite size scaling functions on the aspect ratio can be accounted for by an additional multiplicative factor, we have been able to collapse data for different system sizes, different aspect ratios, and different types of the boundary conditions into a single scaling function $\widehat{\mathcal{Q}}$.

• Received 26 November 2015
• Revised 15 January 2016

DOI:https://doi.org/10.1103/PhysRevE.93.022129