Mixed phases in feedback Ising models

TL;DR

This paper investigates feedback-dependent mean-field Ising models, identifying stable mixed phases at zero temperature, and explores their dynamical behavior under time-varying magnetic fields, providing insights into phase transformations in multistable systems.

Contribution

It introduces feedback Ising models with magnetization-dependent couplings, revealing stable mixed phases and their stability properties, advancing understanding of phase transitions in such systems.

Findings

Stable mixed phases can exist at zero temperature with strong feedback.

Stable mixed phases are super-stable with linear decay of perturbations.

Feedback Ising models can describe phase transformations via intermediate phases.

Abstract

We study mean-field Ising models whose coupling depends on the magnetization via a feedback function. We identify mixed phases (MPs) and show that they can be stable at zero temperature for sufficiently strong feedback. Moreover, stable MPs are always super-stable with perturbation decaying linearly in time. We argue that such feedback Ising models (FIMs) provide a useful framework for phase transformations between aligned phases via stable and unstable intermediate phases in multistable systems. We also analyze the dynamical behavior of FIMs driven by a time-varying magnetic field.