Random-Field Ising Models of Hysteresis

Abstract

This is a review article of our work on hysteresis, avalanches, and criticality. We provide an extensive introduction to scaling and renormalization-group ideas, and discuss analytical and numerical results for size distributions, correlation functions, magnetization, avalanche durations and average avalanche shapes, and power spectra. We focus here on applications to magnetic Barkhausen noise, and briefly discuss non-magnetic systems with hysteresis and avalanches.

Shear-induced rigidity in athermal materials: A unified statistical framework

“…We model this by the zero-temperature, single-spin flips, energy minimizing dynamics of the energy function ( Fig. 1) [19][20][21]:…”

“…Our model, therefore, differs from other driven-disordered models in the class of Eq. 5 [21] in one crucial respect: the external field controls the average population of S i = 0 sites through a chemical potential (∆(H)). For the current study, we model the H dependence of ∆ as ∆ = α|H| + ∆ 0 , which is the simplest that admits an increase in the concentration of S i = 0 with the magnitude of the driving field.…”

“…At a certain H, however, a threshold is crossed at some site i (determined by the h i and the effective field j J ij S j ) and that spin changes its state. This, in turn, could lead to the threshold being crossed at other sites, creating a cascade of spin flips in an avalanche [21] until a new metastable state is reached.…”

Model for domain wall avalanches in ferromagnetic thin films

“…[8] In such systems the more accepted structure is that of Bloch, where the magnetization rotates through of wall, outside of the plane of the magnetic moments. The statistical properties of the DW avalanches are understood today by means of depinning transition models, [9,10] that explain very well many experimental results. Models and experiments have been grouped into two universality classes depending on the values of critical exponents, which also verified scaling equalities fully accepted.…”

TheT= 0 random-field Ising model on a Bethe lattice with large coordination number: hysteresis and metastable states

“…This is a model for disordered ferromagnets which is relevant to a large class of materials where disorder induces random fields [5]. With the standard Glauber dynamics (which does satisfy the nopassing rule at T = 0 [2]), the metastable states are the so-called single-spin-flip stable states, each state being characterized by its energy and magnetization.…”