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

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  • F. Detcheverry
  • M. L. Rosinberg
  • G. Tarjus

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

Suggested Citation

  • F. Detcheverry & M. L. Rosinberg & G. Tarjus, 2005. "Metastable states and T=0 hysteresis in the random-field Ising model on random graphs," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 44(3), pages 327-343, April.
    • Handle: RePEc:spr:eurphb:v:44:y:2005:i:3:p:327-343
    DOI: 10.1140/epjb/e2005-00132-5
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