Metastable states and T=0 hysteresis in the random-field Ising model on random graphs

F. Detcheverry, M. L. Rosinberg () and G. Tarjus

The European Physical Journal B: Condensed Matter and Complex Systems, 2005, vol. 44, issue 3, 327-343

Abstract: We study the ferromagnetic random-field Ising model on random graphs of fixed connectivity z (Bethe lattice) in the presence of an external magnetic field H. We compute the number of single-spin-flip stable configurations with a given magnetization m and study the connection between the distribution of these metastable states in the H-m plane (focusing on the region where the number is exponentially large) and the shape of the saturation hysteresis loop obtained by cycling the field between -∞ and +∞ at T=0. The annealed complexity ΣA(m,H) is calculated for z=2,3,4 and the quenched complexity ΣQ(m,H) for z=2. We prove explicitly for z=2 that the contour ΣQ(m,H)=0 coincides with the saturation loop. On the other hand, we show that ΣA(m,H) is irrelevant for describing, even qualitatively, the observable hysteresis properties of the system. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2005

Date: 2005
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DOI: 10.1140/epjb/e2005-00132-5

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