The T = 0 random-field Ising model on a Bethe lattice with large coordination number: hysteresis and metastable states
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In order to elucidate the relationship between rate-independent hysteresis and metastability in disordered systems driven by an external field, we study the Gaussian RFIM at T = 0 on regular random graphs (Bethe lattice) of finite connectivity z and compute to O(1/z) (i.e. beyond mean field) the quenched complexity associated with the one-spin-flip stable states with magnetization m as a function of the magnetic field H. When the saturation hysteresis loop is smooth in the thermodynamic limit, we find that it coincides with the envelope of the typical metastable states (the quenched complexity vanishes exactly along the loop and is strictly positive everywhere inside). On the other hand, the occurrence of a jump discontinuity in the loop (associated with an infinite avalanche) can be traced back to the existence of a gap in the magnetization of the metastable states for a range of applied fields, and the envelope of the typical metastable states is then reentrant. These findings confirm and complete earlier analytical and numerical studies. Available from http://dx.doi.org/10.1088/1742-5468/2009/03/P03003
RightsRosinberg, M.L., Tarjus, G. and Perez-Reche, F.J. 2009. The T = 0 random-field Ising model on a Bethe lattice with large coordination number: hysteresis and metastable states. Journal of Statistical Mechanics: Theory and Experiment. 2009: P03003. Available from http://dx.doi.org/10.1088/1742-5468/2009/03/P03003. This is an author-created, un-copyedited version of an article accepted for publication in Journal of Statistical Mechanics: Theory and Experiment. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The definitive publisher-authenticated version is available online at DOI: 10.1088/1742-5468/2009/03/P03003.
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