基于泛函RG的钉扎流形热态混沌
Chaos in the thermal regime for pinned manifolds via functional RG
摘要：
本文利用泛函重整化群研究了d维弹性流形的两个拷贝嵌入在稍有不同的冻结无序中的统计相关性，其精度为O（eps = 4-d）.确定相互关联的初始（短尺度）增长，即混沌指数，需要在一个非常微妙的边界层制度的耦合微分（FRG）方程（重正化相互和自无序扩散）的系统的控制。在非零温度下取得了一些进展，其中可以使用线性分析。增长指数a由二次势中的质心波动定义。在温度是边际的情况下，例如d=2的周期流形，我们用解析和数值方法证明了a = eps（1/3 - 1/（2 log（1/T），在低T下有有趣的和意想不到的对数修正。对于短程（随机键）无序，我们的分析表明a = 0.083346（6）eps，具有大的有限尺寸校正。
英文摘要：
The statistical correlations of two copies of a d-dimensional elastic manifold embedded in slightly different frozen disorder are studied using the Functional Renormalization Group to one-loop accuracy, order O(eps = 4-d). Determining the initial (short scale) growth of mutual correlations, i.e. chaos exponents, requires control of a system of coupled differential (FRG) equations (for the renormalized mutual and self disorder correlators) in a very delicate boundary layer regime. Some progress is achieved at non-zero temperature, where linear analysis can be used. A growth exponent a is defined from center of mass fluctuations in a quadratic potential. In the case where temperature is marginal, e.g. a periodic manifold in d=2, we demonstrate analytically and numerically that a = eps (1/3 - 1/(2 log(1/T)) with interesting and unexpected logarithmic corrections at low T. For short range (random bond) disorder our analysis indicates that a = 0.083346(6) eps, with large finite size corrections.
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