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

TL;DR

This paper analytically explores the energy landscape and metastable states of the zero-temperature mean-field soft-spin RFIM, revealing how disorder influences phase transitions and hysteresis behavior.

Contribution

It provides an analytical computation of the quenched complexity of metastable states in the soft-spin RFIM, highlighting disorder-dependent shape changes and phase transition phenomena.

Findings

Complexity region becomes non-convex at low disorder.

Phase transitions occur along the hysteresis loop.

Response differs when magnetization is externally controlled.

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.