Hysteresis and Avalanches in the Random Field Ising Model

Abstract

For Abstract see ChemInform Abstract in Full Text.

Gaps between avalanches in one-dimensional random-field Ising models

“…Here there are several avalanches with a distribution of sizes at different field strengths H. There is, however, a qualitative difference in the nature of avalanches for the cases R > 2J and J < R ≤ 2J [19]. The form of G(1, H) for these two 5), (11) and (19). The points represent data obtained from simulations.…”

“…6 we plot P (∆H) computed using Eqs. (8), (11) and (19) for various values of the disorder strength R at different system sizes. We find that this distribution obeys the scaling form given in Eq.…”

“…To do this we consider a system starting at H 1 and compute the distribution of gaps between events as the field is increased up to H 2 > H 1 . We first compute the cumulative probability S( with coordination number z at zero temperature, reproducing the work of Sabhapandit et al [19,24]. The case z = 2 reduces to the one dimensional model considered in Section III.…”

“…It is therefore worthwhile to study models where one can compute the density of avalanches exactly. In Section III we study the one-dimensional nearest-neighbor ferromagnetic RFIM, where we use the techniques developed in [19] along with the formalism developed in this section to compute P (∆H|H) exactly.…”

“…The ferromagnetic RFIM has several intriguing properties, such as a no-crossing property [22], an Abelian property and a return point memory [23], that make it theoretically accessible [19,24]. For the nearest neighbor RFIM on a Bethe lattice it is indeed possible to compute the probability of an avalanche of size s originating from a given site P (s, H) exactly [19]. It is easy to see that one can then compute the coarse grained density of avalanche events ρ(H).…”