The T=0 random-field Ising model on a Bethe lattice with large coordination number: hysteresis and metastable states

Abstract

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 positive everywhere inside). On the other hand, the occurence 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 field, and the envelope of the typical metastable states is then reentrant. These findings confirm and complete earlier analytical and numerical studies.

29 pages, 9 figures

References in corpus (13)

• Hysteresis and hierarchies: dynamics of disorder-driven first-order phase transformations
• Hysteresis, Avalanches, and Disorder Induced Critical Scaling: A Renormalization Group Approach
• Optimisation problems and replica symmetry breaking in finite connectivity spin-glasses
• Zero-temperature Hysteresis in Random-field Ising Model on a Bethe Lattice
• Driving-induced crossover: from classical criticality to self-organized criticality
• Hysteresis in the Random Field Ising Model and Bootstrap Percolation
• Distribution of Avalanche Sizes in the Hysteretic Response of Random Field Ising Model on a Bethe Lattice at Zero Temperature
• Morphology transitions in three-dimensional domain growth with Gaussian random fields
• Influence of the driving mechanism on the response of systems with athermal dynamics: the example of the random-field Ising model
• Metastable states and T=0 hysteresis in the random-field Ising model on random graphs
• Metastable configurations of spin models on random graphs
• Zero Temperature Hysteresis in Random Field Ising Model on Bethe Lattices: approach to mean field behavior with increasing coordination number z
• Stable, metastable and unstable states in the mean-field RFIM at T=0

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