Mixed phases in feedback Ising models

Yi-ping Ma; Ivan Sudakow; Paul Krapivsky

doi:10.1103/3ck1-gzzf

Mixed phases in feedback Ising models

Yi-ping Ma^*, Ivan Sudakow^*, Paul Krapivsky

^*Corresponding author for this work

School of Engineering Physics and Mathematics

Research output: Contribution to journal › Article › peer-review

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Abstract

We study mean-field Ising models in which the 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, meaning that perturbations decay linearly in time. 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 varying magnetic field and discuss basic properties of finite-dimensional FIMs.

Original language	English
Article number	027101
Number of pages	9
Journal	Physical Review Letters
Volume	137
Issue number	2
DOIs	https://doi.org/10.1103/3ck1-gzzf
Publication status	Published - 7 Jul 2026

Research Group keywords

Mathematics of Complex and Nonlinear Phenomena Group (MC&NPG)

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abstract = "We study mean-field Ising models in which the 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, meaning that perturbations decay linearly in time. 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 varying magnetic field and discuss basic properties of finite-dimensional FIMs.",

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AB - We study mean-field Ising models in which the 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, meaning that perturbations decay linearly in time. 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 varying magnetic field and discuss basic properties of finite-dimensional FIMs.

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Mixed phases in feedback Ising models

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