Hysteresis and complexity in the zero-temperature mean-field RFIM: the soft-spin version

Abstract

We study the energy landscape of the soft-spin random field model in the mean-field limit and compute analytically the quenched complexity of the metastable states as a function of their magnetization and energy at a given external magnetic field. The shape of the domain within which the complexity is positive (and the number of typical metastable states grows exponentially with system size) changes with the amount of disorder and becomes non-convex and disconnected at low disorder. As a consequence, phase transitions occur both at equilibrium and out of equilibrium along the saturation hysteresis loop. We focus on the zero complexity curve in the field-magnetization plane and its relationship with the hysteresis loop. We also study the response of the system when the magnetization is externally controlled instead of the magnetic field. The main features of the model that should survive in finite dimensions are discussed.

15 pages, 10 figures

References in corpus (5)

• Driving-induced crossover: from classical criticality to self-organized criticality
• Influence of the driving mechanism on the response of systems with athermal dynamics: the example of the random-field Ising model
• The T=0 random-field Ising model on a Bethe lattice with large coordination number: hysteresis and metastable states
• The magnetization-driven random field Ising model at T=0
• Stable, metastable and unstable states in the mean-field RFIM at T=0

Cited by in corpus (4)

• On-Site Potential Creates Complexity in Systems with Disordered Coupling
• A statistical mechanical description of metastable states and hysteresis in the 3D soft-spin random-field model at T=0
• Hysteresis and return point memory in the random field Blume Capel model
• Emergence of a random field at the yielding transition of a mean-field Elasto-Plastic model