Disorder in non-equilibrium models
Disorder in non-equilibrium models
复制标题
非平衡模型中的无序
DOI：
10.1088/0953-8984/14/7/306
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发表时间：
2002
期刊：
影响因子：
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通讯作者：
R. Stinchcombe
中科院分区：
文献类型：
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作者：
R. Stinchcombe
概述了存在无序情况下的非平衡系统，这通常会强烈影响其行为。这里考虑的例子是目前正在取得最大进展的例子，即具有替代无序的基于晶格的排除类型的低维集体模型。讨论了局域化等效应，以及稳态非平衡转变时无序诱导的新临界或奇异行为的交叉，以及新的渐近或临界动力学。无序量子自旋系统的映射用于提供一些精确的结果（利用戈德斯通对称性或自由费米子等价），并引入类似于格里菲斯相和麦科伊-吴奇点的非平衡/无序效应。这里还讨论的其他主题包括交叉的标准、非平衡跃迁以及稀释的和可能的尺度不变背景上的动力学。除了映射之外，还使用各种直接方法，例如平均场方法和通常缩放无序分布的缩放程序。当运动方程是线性的或可通过此处介绍的某些变换线性化时，非平衡动力学的缩放相对简单且非常有效。简要讨论了针对更具抵抗力的非线性情况的缩放方法的当前情况。
An overview is presented of non-equilibrium systems in the presence of disorder, which typically strongly affects their behaviour. The examples considered here are those for which most progress is currently being made, namely low-dimensional collective models of the lattice-based exclusion type with substitutional disorder. Discussions are given of such effects as localization, and of disorder-induced crossovers to new critical or singular behaviour at steady state non-equilibrium transitions, and to new asymptotic or critical dynamics. Mappings to disordered quantum spin systems are used to provide some exact results (exploiting Goldstone symmetries or free fermion equivalences) and to introduce non-equilibrium/disorder effects analogous to Griffiths phases and McCoy-Wu singularities. Among other topics also discussed here are criteria for crossovers, and non-equilibrium transitions and dynamics on diluted and possibly scale-invariant backgrounds. As well as mappings, direct approaches of various sorts are used, such as mean field methods, and scaling procedures typically scaling a disorder distribution. Scaling for the non-equilibrium dynamics is relatively simple and very effective when the equations of motion are linear or linearizable by certain transformations presented here. The current situation regarding scaling approaches to the more resistant non-linear cases is briefly discussed.