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

M. L. Rosinberg; G. Tarjus

doi:10.1088/1742-5468/2010/12/p12011

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arXiv · 1009.5008

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

M. L. Rosinberg·G. Tarjus

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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.

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M. L. Rosinberg, G. Tarjus. 2010-09-25. A statistical mechanical description of metastable states and hysteresis in the 3D soft-spin random-field model at T=0. https://doi.org/10.1088/1742-5468%2F2010%2F12%2Fp12011

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