发表机构
Hiroshima Prefectural Fukuyama Seishikan Senior High School（广岛县福山圣城馆高等学校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究全局耦合Ising-Kuramoto模型，发现记忆效应导致同步阈值在有限切换速率下最小化，并给出内部最优条件，模拟验证非单调阈值与模式混合。
AI 中文摘要
我们研究了一个全局耦合的随机系统，其中每个单元携带一个Ising自旋和一个连续相位。自旋以弛豫率$\gamma$经历Glauber切换，而相位由具有相关时间$\tau$的Ornstein-Uhlenbeck噪声驱动。自旋依赖的相位相互作用支持一个复合相干模式，$Z_m=N^{-1}\sum_j\sigma_j e^{i\theta_j}$，即使在普通相位相干性较小时也能有序化。关于非磁性非相干态的线性响应给出同步阈值$K_{\mathrm c}=[(\mu+\beta_s\gamma)\chi_\gamma]^{-1}$，其中$\chi_\gamma$是自由相位相关函数的记忆加权拉普拉斯变换。增加的Glauber响应与减小的记忆磁化率之间的竞争产生一个有限的切换速率，在该速率下$K_{\mathrm c}$被最小化。我们推导了这种内部最优值的一般充分条件，并表明有限时间Ornstein-Uhlenbeck相关性满足所需的快速切换渐近性，而白噪声极限则不一定。有限尺寸模拟再现了非单调阈值、随着$\tau$增加阈值向更慢切换的移动、非磁性状态下的反相复合有序以及磁化背景上的模式混合。
英文摘要
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, $Z_m=N^{-1}\sum_jσ_j e^{iθ_j}$, that can order even when the ordinary phase coherence is small. Linear response about the nonmagnetic incoherent state gives the synchronization threshold $K_{\mathrm c}=[(μ+β_sγ)χ_γ]^{-1}$, 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 $K_{\mathrm c}$ 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.
Comments6 pages, 4 figures
