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 104 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