一级动力学相变的有限尺寸标度：自适应种群动力学和一个有效模型
Finite-Size Scaling of a First-Order Dynamical Phase Transition: Adaptive Population Dynamics and an Effective Model
摘要：
我们分析了一维Fredrickson-Andersen模型中时均活度的大偏差，包括数值分析和解析分析。该模型表现出一个动态的相变，这似乎是一个奇异的大偏差函数。我们分析了这个相变的有限尺寸标度的数值，通过推广现有的克隆算法，包括多正则反馈控制：这显着提高了计算效率。受这些数值结果的启发，我们制定了一个有效的理论模型附近的相变，这占定量观察到的行为。我们讨论的数值方法和有效的理论在一系列更一般的背景下的潜在应用。
英文摘要：
We analyze large deviations of the time-averaged activity in the one dimensional Fredrickson-Andersen model, both numerically and analytically. The model exhibits a dynamical phase transition, which appears as a singularity in the large deviation function. We analyze the finite-size scaling of this phase transition numerically, by generalizing an existing cloning algorithm to include a multi-canonical feedback control: this significantly improves the computational efficiency. Motivated by these numerical results, we formulate an effective theory for the model in the vicinity of the phase transition, which accounts quantitatively for the observed behavior. We discuss potential applications of the numerical method and the effective theory in a range of more general contexts.
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