We revisit the effects of short-ranged random quenched disorder on the universal scaling properties of the classical $N$-vector model with cubic anisotropy. We set up the nonconserved relaxational dynamics of the model, and study the universal dynamic scaling near the second-order phase transition. We extract the critical exponents and the dynamic exponent in a one-loop dynamic renormalization group calculation with short-ranged isotropic disorder. We show that the dynamics near a critical point is generically slower when the quenched disorder is relevant than when it is not, independent of whether the pure model is isotropic or cubic anisotropic. We demonstrate the surprising thresholdless instability of the associated universality class due to perturbations from rotational invariance breaking quenched disorder-order parameter coupling, indicating breakdown of dynamic scaling. We speculate that this may imply a novel first-order transition in the model, induced by a symmetry-breaking disorder.

中文翻译：

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失调的无序经典N向量模型中的动态缩放

我们回顾了短程随机淬火失调对经典的普遍缩放性质的影响 $ñ$立方各向异性的矢量模型。我们建立了模型的非保守弛豫动力学，并研究了二阶相变附近的普遍动力学尺度。我们在短程各向同性无序的一环动态重归一化组计算中提取临界指数和动态指数。我们表明，当淬火紊乱相关时，临界点附近的动力学通常较慢，而不是不相关，这与纯模型是各向同性还是立方各向异性无关。我们证明了相关的通用性类的令人惊讶的无阈值不稳定性，原因是来自旋转不变性的扰动打破了失稳的无序阶参数耦合，表明了动态缩放的崩溃。我们推测这可能意味着模型中出现了新颖的一阶转换，