Memory-induced optimal switching in a dynamic Ising-Kuramoto model
Abstract
We study a globally coupled stochastic system in which each unit carries an Ising spin and a continuous phase. The spins undergo Glauber switching with relaxation rate γ, while the phases are driven by Ornstein-Uhlenbeck noise with correlation time τ. A spin-dependent phase interaction supports a composite coherent mode, Zm=N−1∑jσj eiθj, that can order even when the ordinary phase coherence is small. Linear response about the nonmagnetic incoherent state gives the synchronization threshold Kc=[(μ+βsγ)χγ]−1, where χγ is a memory-weighted Laplace transform of the free phase correlation function. The competition between the increasing Glauber response and the decreasing memory susceptibility produces a finite switching rate at which Kc is minimized. We derive a general sufficient condition for such an interior optimum and show that finite-time Ornstein-Uhlenbeck correlations satisfy the required fast-switching asymptotics, whereas the white-noise limit need not. Finite-size simulations reproduce the nonmonotonic threshold, its shift toward slower switching as τ increases, antiphase composite order in a nonmagnetic state, and mode mixing on a magnetized background.
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BibTeX
@misc{hayashi2026memoryinduced,
title = {{Memory-induced optimal switching in a dynamic Ising-Kuramoto model}},
author = {Reon Hayashi},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.35838},
eprint = {2609.35838},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.35838},
}
RIS
TY - UNPB
TI - Memory-induced optimal switching in a dynamic Ising-Kuramoto model
AU - Reon Hayashi
PY - 2026
DA - 2026/09/24
PB - arXiv
DO - 10.48550/arxiv.2609.35838
UR - https://arxiv.org/abs/2609.35838
AB - We study a globally coupled stochastic system in which each unit carries an Ising spin and a continuous phase. The spins undergo Glauber switching with relaxation rate γ, while the phases are driven by Ornstein-Uhlenbeck noise with correlation time τ. A spin-dependent phase interaction supports a composite coherent mode, Z_m=N^−1∑_jσ_j e^iθ_j, that can order even when the ordinary phase coherence is small. Linear response about the nonmagnetic incoherent state gives the synchronization threshold K_c=[(μ+β_sγ)χ_γ]^−1, where χ_γ is a memory-weighted Laplace transform of the free phase correlation function. The competition between the increasing Glauber response and the decreasing memory susceptibility produces a finite switching rate at which K_c is minimized. We derive a general sufficient condition for such an interior optimum and show that finite-time Ornstein-Uhlenbeck correlations satisfy the required fast-switching asymptotics, whereas the white-noise limit need not. Finite-size simulations reproduce the nonmonotonic threshold, its shift toward slower switching as τ increases, antiphase composite order in a nonmagnetic state, and mode mixing on a magnetized background.
ER -