Nonperturbative renormalization group for the stationary Kardar-Parisi-Zhang equation: scaling functions and amplitude ratios in 1+1, 2+1, and 3+1 dimensions.
Nonperturbative renormalization group for the stationary Kardar-Parisi-Zhang equation: scaling functions and amplitude ratios in 1+1, 2+1, and 3+1 dimensions.
复制标题
平稳 Kardar-Parisi-Zhang 方程的非微扰重正化群：1 1、2 1 和 3 1 维中的缩放函数和振幅比。
DOI：
10.1103/physreve.86.051124
复制
发表时间：
2012
期刊：
影响因子：
--
通讯作者：
N. Wschebor
中科院分区：
文献类型：
--
作者：
T. Kloss;L. Canet;N. Wschebor
我们研究了强耦合制度的定态Kardar-Parisi-Zhang方程的界面上生长的尺寸d = 1，2和3使用非微扰重整化群（NPRG）的方法。我们计算临界指数，相关性和响应函数，提取相关的标度函数，并计算通用振幅比。我们使用先前工作[Phys. Rev. E 84，061150（2011）和Phys. Rev. E 86，019904（E）（2012）]中提出的二阶（响应场中）近似的简化实现，这大大简化了NPRG流方程的频率部分，同时保持了两点函数的非平凡频率依赖性。在这种方法中得到的一维尺度函数比较非常准确的尺度函数从完整的二阶NPRG方程和精确的尺度函数。此外，该方法是很容易适用于更高的维度，我们提供的标度函数和振幅比在d = 2和d = 3。我们认为我们的证明在d [符号：见正文] 3.5之前是可靠的。
We investigate the strong-coupling regime of the stationary Kardar-Parisi-Zhang equation for interfaces growing on a substrate of dimension d = 1, 2, and 3 using a nonperturbative renormalization group (NPRG) approach. We compute critical exponents, correlation and response functions, extract the related scaling functions, and calculate universal amplitude ratios. We work with a simplified implementation of the second-order (in the response field) approximation proposed in a previous work [Phys. Rev. E 84, 061150 (2011) and Phys. Rev. E 86, 019904(E) (2012)], which greatly simplifies the frequency sector of the NPRG flow equations, while keeping a nontrivial frequency dependence for the two-point functions. The one-dimensional scaling function obtained within this approach compares very accurately with the scaling function obtained from the full second-order NPRG equations and with the exact scaling function. Furthermore, the approach is easily applicable to higher dimensions and we provide scaling functions and amplitude ratios in d = 2 and d = 3. We argue that our ansatz is reliable up to d [Symbol: see text] 3.5.
影响因子：
1.6
作者：
K. Takeuchi;M. Sano
通讯作者：
K. Takeuchi;M. Sano