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

### L. X. Hayden, Archishman Raju, James P. Sethna

### 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 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 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.

## Normal form for renormalization groups

### Archishman Raju, Colin B. Clement, Lorien X. Hayden, Jaron P. Kent-Dobias, Danilo B. Liarte, D. Zeb Rocklin, James P. Sethna

## Jeffrey's prior sampling of deep sigmoidal networks

### Lorien X. Hayden, Alexander A. Alemi, Paul H. Ginsparg, James P. Sethna

## Deformation of crystals: Connections with statistical physics

### James P. Sethna, Matthew K. Bierbaum, Karin A. Dahmen, Carl P. Goodrich, Julia R. Greer, Lorien X. Hayden, Jaron P. Kent-Dobias, Edward D. Lee, Danilo B. Liarte, Xiaoyue Ni, Katherine N. Quinn, Archishman Raju, D. Zeb Rocklin, Ashivni Shekhawat, Stefano Zapperi

## Canonical Sectors and Evolution of Firms in the US Stock Markets

### Lorien X. Hayden, Ricky Chachra, Alexander A. Alemi, Paul H. Ginsparg, James P. Sethna

## Intrinsic Spin Hall Effect at Oxide Interfaces: a Simple Model

### Lorien H. Hayden, R. Raimondi, M. E. Flatte', G. Vignale

## Macrospin Tunneling and Magnetopolaritons with Nanomechanical Interference

### Alexey A. Kovalev, Lorien X. Hayden, Gerrit E. W. Bauer, Yaroslav Tserkovnyak

## Frustrated classical Heisenberg and XY models in 2 dimensions with nearest neighbor exchange: exact solution for the ground state phase diagram

### L. X. Hayden, T. A. Kaplan, S. D. Mahanti