Noise in Disordered Systems: Higher Order Spectra in Avalanche Models

TL;DR

This paper introduces a new analytical approach to calculating higher order spectra in mean field avalanche models and validates it with simulations, revealing novel exponents in disordered systems.

Contribution

It provides the first analytical calculation of Haar power spectra and higher order spectra for mean field avalanche models, supported by simulation results.

Findings

Analytical expressions for Haar power spectra and higher order spectra.

Simulation results for zero-temperature RFIM in three dimensions.

Discovery of novel exponents in spectral analysis.

Abstract

We present a novel analytic calculation of the Haar power spectra, and various higher order spectra, of mean field avalanche models. We also compute these spectra from a simulation of the zero-temperature mean field RFIM and infinite range RFIM model for $d = 3$. We compare the results and obtain novel exponents.