轻-重模型中的临界行为与交叉标度
Critical behavior and crossover scaling in the Light-Heavy model
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中文总结 AI 辅助
本文研究轻-重（LH）模型的临界行为与交叉标度，分析其未标度（uLH）区域的FDPO相变、局部类FDPO行为，及标度（sLH）区域的单模式动力学与反常长程关联，并类比sABC模型推导关联函数解析表达式。
中文摘要 AI 辅助
轻-重（Light-Heavy, LH）模型包含两种粒子（轻粒子与重粒子），它们与涨落表面（由倾斜角描述）耦合。其动力学既包括粒子（或倾斜角）的固有扩散，也包括由倾斜角（或粒子）提供的驱动。当两者大小相近时，系统处于未标度（unscaled, uLH）区域；而当驱动显著较弱时，系统处于标度（scaled, sLH）区域。在未标度极限下，该模型表现出由涨落主导的相序（fluctuation-dominated phase ordering, FDPO）所表征的有序-无序相变。值得注意的是，在此状态下，动力学由多种模式驱动，从而产生动态团簇。在远离临界区域时，无序相在小于关联长度的长度尺度上仍保留FDPO行为的痕迹。我们通过使用一个连接非临界区域与临界区域的标度函数，研究了这种类局部FDPO行为。接下来我们转向标度模型，结果表明，在未标度区域存在的多模式动力学，在标度区域被有效由单一主导模式控制的动力学所取代。与此同时，两点关联从O(1)的FDPO形式转变为以1/√L衰减的反常长程形式。借助与在临界点处出现类似反常关联的sABC模型的类比，我们采用与该模型相同的方法推导出了两点关联函数的解析表达式。
英文摘要
The Light-Heavy (LH) model involves two species of particles (light and heavy) coupled with a fluctuating surface (described by tilts). The dynamics include the inherent diffusion of the particles (or tilts) as well as the drive provided by the tilts (or particles). When the two are of similar magnitude, the system lies in the unscaled (uLH) regime, while a significantly weaker drive leads to the scaled (sLH) regime. In the unscaled limit, the model exhibits an order-disorder transition characterized by the fluctuation-dominated phase ordering (FDPO). In this state, interestingly the dynamics is driven by multiple modes, giving rise to dynamic clusters. Away from the critical regime the disordered phase retains vestiges of FDPO behavior on length scales smaller than the correlation length. We examine this local FDPO-like behavior by using a scaling function that links the off-critical and critical regimes. We next turn to the scaled model and show that the multi-mode dynamics present in the unscaled regime is replaced by dynamics that is effectively controlled by a single dominant mode in the scaled regime. Concurrently, the two-point correlations change from the $\mathcal{O}(1)$ FDPO form to an anomalous long-range form that decays as $1/\sqrt{L}$. Drawing on the analogy with the sABC model, where similar anomalous correlations appear at criticality, we derive an analytical expression for the two-point correlation function using the same approach used for that model.
