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

TL;DR

This study investigates how aspect ratio and boundary conditions influence universal finite size scaling functions in the 2D Random Field Ising Model at zero temperature, revealing a unified scaling function that accounts for these factors.

Contribution

It introduces a new scaling variable and a multiplicative factor to collapse data across different system sizes, aspect ratios, and boundary conditions into a single universal function.

Findings

Data collapse achieved for various system sizes and boundary conditions.

Universal scaling function Q successfully describes the finite size effects.

Aspect ratio significantly affects the finite size scaling behavior.

Abstract

This work studies universal finite size scaling functions for the number of 1d spanning avalanches in a two-dimensional disordered system with boundary conditions of different nature and different aspect ratios. For this purpose, we 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 choose a convenient scaling variable z that accounts for the deformation of the distance to the critical point caused by the aspect ratio. Moreover, assuming that the dependence of the finite size scaling functions on the aspect ratio can be accounted by an additional multiplicative factor, we have been able to collapse data for different system sizes, different aspect ratios and different nature of the boundary conditions into a single scaling function Q.