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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.07301 |
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| _version_ | 1866908921580486656 |
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| author | Ma, Yi-Ping Sudakow, Ivan Krapivsky, P. L. Vakulenko, Sergey A. |
| author_facet | Ma, Yi-Ping Sudakow, Ivan Krapivsky, P. L. Vakulenko, Sergey A. |
| contents | We study the dynamics of a mean-field Ising model whose coupling depends on the magnetization via a linear feedback function. A key feature of this linear feedback Ising model (FIM) is the possibility of temperature-induced bistability, where a temperature increase can favor bistability between two phases. We show that the linear FIM provides a minimal model for a transcritical bifurcation as the temperature varies. Moreover, there can be two or three critical temperatures when the external magnetic field is non-negative. In the bistable region, we identify a Maxwell temperature where the two phases are equally probable, and we find that increasing the temperature favors the lower phase. We show that the probability distribution becomes non-Gaussian on certain time intervals when the magnetization converges algebraically at either zero temperature or critical temperatures. Near critical points in the parameter space, we derive a Fokker-Planck equation, construct the families of equilibrium distributions, and formulate scaling laws for transition rates between two stable equilibria. The linear FIM offers considerable flexibility in controlling steady-state bifurcations and their associated equilibrium distributions, which can be desirable for modeling feedback systems across various disciplines. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_07301 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Dynamics of feedback Ising model Ma, Yi-Ping Sudakow, Ivan Krapivsky, P. L. Vakulenko, Sergey A. Statistical Mechanics Dynamical Systems We study the dynamics of a mean-field Ising model whose coupling depends on the magnetization via a linear feedback function. A key feature of this linear feedback Ising model (FIM) is the possibility of temperature-induced bistability, where a temperature increase can favor bistability between two phases. We show that the linear FIM provides a minimal model for a transcritical bifurcation as the temperature varies. Moreover, there can be two or three critical temperatures when the external magnetic field is non-negative. In the bistable region, we identify a Maxwell temperature where the two phases are equally probable, and we find that increasing the temperature favors the lower phase. We show that the probability distribution becomes non-Gaussian on certain time intervals when the magnetization converges algebraically at either zero temperature or critical temperatures. Near critical points in the parameter space, we derive a Fokker-Planck equation, construct the families of equilibrium distributions, and formulate scaling laws for transition rates between two stable equilibria. The linear FIM offers considerable flexibility in controlling steady-state bifurcations and their associated equilibrium distributions, which can be desirable for modeling feedback systems across various disciplines. |
| title | Dynamics of feedback Ising model |
| topic | Statistical Mechanics Dynamical Systems |
| url | https://arxiv.org/abs/2510.07301 |