耦合球面p自旋系统

中文摘要 AI 辅助

球面p自旋模型为玻璃态动力学提供了平均场框架。耦合此类系统为探究它们如何共同演化、发展互相关以及可能共享共同的老化时间尺度提供了一条可控途径。我们研究了具有位点无关的系统间耦合以及一般相关淬火无序的球面p自旋系统。我们推导了用于关联、响应和球面约束的闭合的多子系统双时方程。一个边缘的一步复制对称破缺构造为重叠平台、老化交叉时间尺度和有效温度提供了静态基准。然后我们专门研究两个铁磁耦合的p=3系统，并将动力学数据与边缘1RSB预测进行比较。独立的淬火无序将系统间的等时关联降低到其无无序值以下，而相关的无序则增强该关联。对于足够强的耦合，系统内部和系统之间的有限时间涨落耗散估计与共同的有效温度相容，即使一个或两个子系统在孤立时作为顺磁体平衡。该共同值高于各组成系统单独具有的有效温度，并随无序相关性和耦合强度而增加。边缘1RSB值T/m捕捉了这些趋势，但略低于有限时间动力学估计。对于弱耦合，动力学结果反而表明每个系统发展出两个老化区域，每个区域内部分平衡。我们进行了具有两步破缺的边缘复制分析，其预测与数值测量结果相符良好。我们的数值精度不足以确定观察到的有限时间交叉是否最终会变成尖锐的转变。

英文摘要

Spherical p-spin models provide a mean-field framework for glassy dynamics. Coupling such systems opens a controlled way to probe how they evolve jointly, develop cross correlations, and possibly share common aging scales. We study spherical p-spin systems with site-independent inter-system couplings and generally correlated quenched disorders. We derive closed multi-subsystem two-time equations for correlations, responses, and spherical constraints. A marginal one-step replica-symmetry-breaking construction provides static benchmarks for overlap plateaux, aging crossover scales, and effective temperatures. We then specialize to two ferromagnetically coupled p=3 systems and compare dynamical data with marginal 1RSB predictions. Independent quenched disorders reduce the equal-time correlation between the systems below its disorder-free value, while correlated disorders enhance it. For sufficiently strong coupling, finite-time fluctuation-dissipation estimates within and between the systems are compatible with a common effective temperature even when one or both subsystems would equilibrate as a paramagnet in isolation. This common value lies above the effective temperatures that the constituent systems would have separately and increases with disorder correlation and coupling strength. The marginal 1RSB value T/m captures these trends but is slightly below the finite-time dynamical estimate. For weak coupling, the dynamical results instead suggest that two aging regimes develop for each system, with partial equilibration within each. We perform a marginal replica analysis with two-step breaking, whose predictions compare favorably with the numerical measurements. Our numerical accuracy is insufficient to determine whether the observed finite-time crossover will eventually become a sharp transition.

发表机构

• Sapienza Università di Roma（罗马智慧大学）
• Sorbonne Université（索邦大学）

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