论文标题
抗铁磁$ O（3）$非线性Sigma模型的关键动力学具有保守磁化
Critical Dynamics of the Antiferromagnetic $O(3)$ Nonlinear Sigma Model with Conserved Magnetization
论文作者
论文摘要
我们研究了$ O（3）$非线性sigma模型的近平衡临界动力学，描述了各向同性抗fiferromagnets，其未经保密的有序参数可逆地与保守的总磁化。为了计算响应和相关函数，我们根据Langevin随机运动及其相应的Janssen-De〜Dominicis响应功能来设置描述。我们发现，在平衡中，与静态和动态非线性相对于静态处理，至少在扰动处理中至少与静态分离的动力学分离。由于必须以尺寸$ d = 2 + \ varepsilon $扩展其较低的临界尺寸$ d_ \ d_ \ textrm {lc} = 2 $的静态非线性sigma模型，而动态模式耦合术语则由上限$ d_c = 4 $ dosive fortion forsional notive fortion forsiondion fortion fortion fortion for fortion fortimion for fortion fortions for fortions for fortion for fortions for forsive，该模型无法在静态临界重归其化组固定点上访问。但是，在解决低温有序阶段的长波长属性的共存限制中，我们可以在$ d_c $附近执行$ε= 4- d $扩展。这产生了由无质量金石模式引起的异常缩放特征，即对保守的磁化密度的宽带松弛，并具有渐近缩放尺度指数$z_γ= d -2 $，在中子散射实验中可以观察到。有趣的是，如果在临界点附近初始化，有效动力学指数的重新归一化组流量将在中间交叉区域恢复其通用临界值$ z_c = d / 2 $。
We study the near-equilibrium critical dynamics of the $O(3)$ nonlinear sigma model describing isotropic antiferromagnets with non-conserved order parameter reversibly coupled to the conserved total magnetization. To calculate response and correlation functions, we set up a description in terms of Langevin stochastic equations of motion, and their corresponding Janssen--De~Dominicis response functional. We find that in equilibrium, the dynamics is well-separated from the statics, at least to one-loop order in a perturbative treatment with respect to the static and dynamical nonlinearities. Since the static nonlinear sigma model must be analyzed in a dimensional $d = 2 + \varepsilon$ expansion about its lower critical dimension $d_\textrm{lc} = 2$, whereas the dynamical mode-coupling terms are governed by the upper critical dimension $d_c = 4$, a simultaneous perturbative dimensional expansion is not feasible, and the reversible critical dynamics for this model cannot be accessed at the static critical renormalization group fixed point. However, in the coexistence limit addressing the long-wavelength properties of the low-temperature ordered phase, we can perform an $ε= 4 - d$ expansion near $d_c$. This yields anomalous scaling features induced by the massless Goldstone modes, namely sub-diffusive relaxation for the conserved magnetization density with asymptotic scaling exponent $z_Γ= d - 2$ which may be observable in neutron scattering experiments. Intriguingly, if initialized near the critical point, the renormalization group flow for the effective dynamical exponents recovers their universal critical values $z_c = d / 2$ in an intermediate crossover region.
