A statistical mechanical description of metastable states and hysteresis in the 3D soft-spin random-field model at T=0

TL;DR

This paper develops a statistical mechanical framework to analyze metastable states and hysteresis in the 3D soft-spin random-field model at zero temperature, enabling calculation of hysteresis loops and avalanche statistics without dynamical simulations.

Contribution

It introduces a formalism using replica theory and approximations to compute the complexity and hysteresis loop in finite-dimensional disordered magnetic systems.

Findings

Calculated the hysteresis loop in three dimensions.

Derived correlation functions along the hysteresis loop.

Estimated the second moment of avalanche-size distribution.

Abstract

We present a formalism for computing the complexity of metastable states and the zero-temperature magnetic hysteresis loop in the soft-spin random-field model in finite dimensions. The complexity is obtained as the Legendre transform of the free-energy associated to a certain action in replica space and the hysteresis loop above the critical disorder is defined as the curve in the field-magnetization plane where the complexity vanishes; the nonequilibrium magnetization is therefore obtained without having to follow the dynamical evolution. We use approximations borrowed from condensed-matter theory and based on assumptions on the structure of the direct correlation functions (or proper vertices), such as a local approximation for the self-energies, to calculate the hysteresis loop in three dimensions, the correlation functions along the loop, and the second moment of the avalanche-size distribution.