A statistical mechanical description of metastable states and hysteresis in the 3D soft-spin random-field model at T=0

Abstract

We present a formalism for computing the complexity of metastable states and the zero-temperature magnetic hysteresis loop in the soft-spin random-field model in finite dimensions. The complexity is obtained as the Legendre transform of the free-energy associated to a certain action in replica space and the hysteresis loop above the critical disorder is defined as the curve in the field-magnetization plane where the complexity vanishes; the nonequilibrium magnetization is therefore obtained without having to follow the dynamical evolution. We use approximations borrowed from condensed-matter theory and based on assumptions on the structure of the direct correlation functions (or proper vertices), such as a local approximation for the self-energies, to calculate the hysteresis loop in three dimensions, the correlation functions along the loop, and the second moment of the avalanche-size distribution.

28 pages, 12 figures

References in corpus (6)

• Size distributions of shocks and static avalanches from the Functional Renormalization Group
• Non-Perturbative Functional Renormalization Group for Random Field Models and Related Disordered Systems. I: Effective Average Action Formalism
• Mean field theory for the three-dimensional Coulomb glass
• Evidence for a disorder driven phase transition in the condensation of 4He in aerogels
• Spontaneous versus explicit replica symmetry breaking in the theory of disordered systems
• Hysteresis and complexity in the zero-temperature mean-field RFIM: the soft-spin version

Cited by in corpus (3)

• Criticality of the random field Ising model in and out of equilibrium: a nonperturbative functional renormalization group description
• Same universality class for the critical behavior in and out of equilibrium in a quenched random field
• Emergence of a random field at the yielding transition of a mean-field Elasto-Plastic model