Metastable states and T = 0 hysteresis in the random-field Ising model on random graphs
Laboratoire de Physique Théorique des Liquides, Université Pierre et
Marie Curie, 4 place Jussieu, 75252 Paris Cedex 05, France
Corresponding author: a firstname.lastname@example.org
Published online: 28 April 2005
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 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 is calculated for z=2,3,4 and the quenched complexity for z=2. We prove explicitly for z=2 that the contour coincides with the saturation loop. On the other hand, we show that is irrelevant for describing, even qualitatively, the observable hysteresis properties of the system.
PACS: 75.10.Nr – Spin-glass and other random models / 75.60.Ej – Magnetization curves, hysteresis, Barkhausen and related effects / 05.50.+q – Lattice theory and statistics (Ising, Potts, etc.)
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2005