Canet Léonie, Chaté Hugues, Delamotte Bertrand, Wschebor Nicolás
Laboratoire de Physique et Modélisation des Milieux Condensés, CNRS UMR 5493, Université Joseph Fourier Grenoble I, BP166, F-38042 Grenoble Cedex, France.
Phys Rev E Stat Nonlin Soft Matter Phys. 2011 Dec;84(6 Pt 1):061128. doi: 10.1103/PhysRevE.84.061128. Epub 2011 Dec 15.
We present an analytical method, rooted in the nonperturbative renormalization group, that allows one to calculate the critical exponents and the correlation and response functions of the Kardar-Parisi-Zhang (KPZ) growth equation in all its different regimes, including the strong-coupling one. We analyze the symmetries of the KPZ problem and derive an approximation scheme that satisfies the linearly realized ones. We implement this scheme at the minimal order in the response field, and show that it yields a complete, qualitatively correct phase diagram in all dimensions, with reasonable values for the critical exponents in physical dimensions. We also compute in one dimension the full (momentum and frequency dependent) correlation function, and the associated universal scaling function. We find a very satisfactory quantitative agreement with the exact result from Prähofer and Spohn [J. Stat. Phys. 115, 255 (2004)]. In particular, we obtain for the universal amplitude ratio g_{0}≃1.149(18), to be compared with the exact value g_{0}=1.1504... (the Baik and Rain [J. Stat. Phys. 100, 523 (2000)] constant). We emphasize that all these results, which can be systematically improved, are obtained with sole input the bare action and its symmetries, without further assumptions on the existence of scaling or on the form of the scaling function.
我们提出了一种基于非微扰重整化群的分析方法，该方法能让人们计算 Kardar - Parisi - Zhang（KPZ）增长方程在所有不同区域（包括强耦合区域）的临界指数、关联函数和响应函数。我们分析了 KPZ 问题的对称性，并推导了一种满足线性实现对称性的近似方案。我们在响应场中以最低阶实现该方案，并表明它在所有维度上都能产生一个完整的、定性正确的相图，且物理维度中的临界指数值合理。我们还在一维中计算了完整的（依赖于动量和频率的）关联函数以及相关的普适标度函数。我们发现与Prähofer 和 Spohn [《统计物理杂志》115, 255 (2004)] 的精确结果有非常令人满意的定量一致性。特别是，我们得到普适振幅比(g_{0}\approx1.149(18))，与精确值(g_{0}=1.1504...)（Baik 和 Rain [《统计物理杂志》100, 523 (2000)] 常数）进行比较。我们强调，所有这些结果都可以系统地改进，它们仅通过裸作用及其对称性作为输入得到，而无需对标度的存在或标度函数的形式做进一步假设。
