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Hysteresis Loop Critical Exponents in 6-Epsilon Dimensions

Karin Dahmen·James P. Sethna
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Abstract

The hysteresis loop in the zero-temperature random-field Ising model exhibits a critical point as the width of the disorder increases. Above six dimensions, the critical exponents of this transition, where the "infinite avalanche" first disappears, are described by mean-field theory. We expand the critical exponents about mean-field theory, in 6-epsilon dimensions, to first order in epsilon. Despite epsilon=3, the values obtained agree reasonably well with the numerical values in three dimensions.

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Karin Dahmen, James P. Sethna. 1993-10-15. Hysteresis Loop Critical Exponents in 6-Epsilon Dimensions. https://doi.org/10.1103/physrevlett.71.3222

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