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Hysteresis, Avalanches, and Disorder Induced Critical Scaling: A Renormalization Group Approach

Karin Dahmen·James P. Sethna
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Abstract

We study the zero temperature random field Ising model as a model for noise and avalanches in hysteretic systems. Tuning the amount of disorder in the system, we find an ordinary critical point with avalanches on all length scales. Using a mapping to the pure Ising model, we Borel sum the $6-ε$ expansion to $O(ε^5)$ for the correlation length exponent. We sketch a new method for directly calculating avalanche exponents, which we perform to $O(ε)$. Numerical exponents in 3, 4, and 5 dimensions are in good agreement with the analytical predictions.

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Karin Dahmen, James P. Sethna. 1995-07-26. Hysteresis, Avalanches, and Disorder Induced Critical Scaling: A Renormalization Group Approach. https://doi.org/10.1103/physrevb.53.14872

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