# Weird scaling for 2-D avalanches: Curing the faceting, and scaling in the lower critical dimension

## TL;DR

This paper addresses the challenges of scaling and faceting in 2D non-equilibrium RFIM by using Voronoi lattices and a new RG-based method, revealing a zero critical disorder and confirming two-dimensional lower critical dimension.

## Contribution

The authors introduce two methods—Voronoi lattice simulations and a normal form RG approach—to resolve faceting and scaling issues in 2D RFIM, providing new insights into its critical behavior.

## Key findings

- Scaling collapses cover a wide disorder range
- Critical disorder is zero in 2D RFIM
- Lower critical dimension is confirmed as two

## Abstract

The non-equilibrium random-field Ising model is well studied, yet there are outstanding questions. In two dimensions, power law scaling approaches fail and the critical disorder is difficult to pin down. Additionally, the presence of faceting on the square lattice creates avalanches that are lattice dependent at small scales. We propose two methods which we find solve these issues. First, we perform large scale simulations on a Voronoi lattice to mitigate the effects of faceting. Secondly, the invariant arguments of the universal scaling functions necessary to perform scaling collapses can be directly determined using our recent normal form theory of the Renormalization Group. This method has proven useful in cleanly capturing the complex behavior which occurs in both the lower and upper critical dimensions of systems and here captures the 2D NE-RFIM behavior well. The obtained scaling collapses span over a range of a factor of ten in the disorder and a factor of $10^4$ in avalanche cutoff. They are consistent with a critical disorder at zero and with a lower critical dimension for the model equal to two.