Weird scaling for 2-D avalanches: curing the faceting, and scaling in the lower critical dimension
Abstract
The non-equilibrium random-field Ising model (NE-RFIM) is very well studied and 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 form of the nonlinear 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 well describes the NE-RFIM in two-dimensions. The obtained scaling collapses span over a range of a factor of ten in the disorder and a factor of 104 in avalanche size. They are consistent with a critical disorder at zero and with a lower critical dimension for the model equal to two.
This material is based upon work supported by the National Science Foundation under Grant No. DMR-1719490.- Publication:
-
APS March Meeting Abstracts
- Pub Date:
- 2019
- Bibcode:
- 2019APS..MARV38009H