Yao Louie Hong, Täuber Uwe C
Department of Physics & Center for Soft Matter and Biological Physics, MC 0435, Robeson Hall, 850 West Campus Drive, Virginia Tech, Blacksburg, Virginia 24061, USA.
Phys Rev E. 2022 Jun;105(6-1):064128. doi: 10.1103/PhysRevE.105.064128.
We study the near-equilibrium critical dynamics of the O(3) nonlinear sigma model describing isotropic antiferromagnets with a nonconserved 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+ɛ expansion about its lower critical dimension d_{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 subdiffusive 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.
我们研究了(O(3))非线性西格玛模型的近平衡临界动力学，该模型描述了各向同性反铁磁体，其序参量不守恒且与守恒的总磁化强度可逆耦合。为了计算响应函数和关联函数，我们根据朗之万随机运动方程及其相应的扬森 - 德多米尼斯响应泛函建立了一种描述。我们发现，在平衡状态下，动力学与静力学至少在关于静态和动态非线性的微扰处理中到一圈阶是很好地分离的。由于静态非线性西格玛模型必须在其下临界维度(d_{lc}=2)附近的(d = 2 + \epsilon)展开中进行分析，而动态模式耦合项由上临界维度(d_{c}=4)控制，同时进行微扰维度展开是不可行的，并且该模型的可逆临界动力学无法在静态临界重整化群不动点处得到。然而，在处理低温有序相长波性质的共存极限中，我们可以在(d_{c})附近进行(\epsilon = 4 - d)展开。这产生了由无质量戈德斯通模式引起的反常标度特征，即守恒磁化密度的亚扩散弛豫，其渐近标度指数(z_{\Gamma}=d - 2)，这可能在中子散射实验中观察到。有趣的是，如果在临界点附近初始化，有效动态指数的重整化群流在中间交叉区域恢复其通用临界值(z_{c}=d/2)。
