标题： 稳态剪切流中$O(n)$模型的动力学重整化群分析 显示英文标题

标题： Dynamical renormalization group analysis of $O(n)$ model in steady shear flow

摘要： 我们使用动态重正化群（RG）方法研究稳态剪切流下$O(n)$模型的临界行为。 在尺度假设中引入了之前 RG 分析中被忽略的强各向异性，我们识别出一个新的稳定的高斯固定点。 这个固定点再现了非守恒（模型 A）和守恒（模型 B）序参量的静态和动态临界指数的各向异性标度。 值得注意的是，上限临界维数为$d_{\text{up}} = 2$对于非守恒序参量（模型 A），为$d_{\text{up}} = 0$对于守恒序参量（模型 B），这意味着即使在$d=2$和$3$维度下也会观察到均场临界指数。 此外，所有维度$d \geq 2$下的序参量标度指数为负，表明剪切流即使在$d = 2$中也能稳定与连续对称性破缺相关的长程序。 换句话说，两种类型的序参数的下临界维度都是$d_{\rm low} < 2$。 这与平衡系统不同，在平衡系统中，Hohenberg -- Mermin -- Wagner 定理禁止在$d = 2$中出现连续对称性破缺。 显示英文摘要

摘要： We study the critical behavior of the $O(n)$ model under steady shear flow using a dynamical renormalization group (RG) method. Incorporating the strong anisotropy in scaling ansatz, which has been neglected in earlier RG analyses, we identify a new stable Gaussian fixed point. This fixed point reproduces the anisotropic scaling of static and dynamical critical exponents for both non-conserved (Model A) and conserved (Model B) order parameters. Notably, the upper critical dimensions are $d_{\text{up}} = 2$ for the non-conserved order parameter (Model A) and $d_{\text{up}} = 0$ for the conserved order parameter (Model B), implying that the mean-field critical exponents are observed even in both $d=2$ and $3$ dimensions. Furthermore, the scaling exponent of the order parameter is negative for all dimensions $d \geq 2$, indicating that shear flow stabilizes the long-range order associated with continuous symmetry breaking even in $d = 2$. In other words, the lower critical dimensions are $d_{\rm low} < 2$ for both types of order parameters. This contrasts with equilibrium systems, where the Hohenberg -- Mermin -- Wagner theorem prohibits continuous symmetry breaking in $d = 2$.