Akkineni Vamsi K, Täuber Uwe C
Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801-3080, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2004 Mar;69(3 Pt 2):036113. doi: 10.1103/PhysRevE.69.036113. Epub 2004 Mar 24.
We investigate the critical dynamics of the n-component relaxational models C and D, which incorporate the coupling of a nonconserved and conserved order parameter S, respectively, to the conserved energy density rho, under nonequilibrium conditions by means of the dynamical renormalization group. Detailed balance violations can be implemented isotropically by allowing for different effective temperatures for the heat baths coupling to the slow modes. In the case of model D with conserved order parameter, the energy density fluctuations can be integrated out, leaving no trace of the nonequilibrium perturbations in the asymptotic regime. For model C with scalar order parameter, in equilibrium governed by strong dynamic scaling (z(S)=z(rho)), we find no genuine nonequilibrium fixed point either. The nonequilibrium critical dynamics of model C with n=1 thus follows the behavior of other systems with nonconserved order parameter wherein detailed balance becomes effectively restored at the phase transition. For n> or =4, the energy density generally decouples from the order parameter. However, for n=2 and n=3, in the weak dynamic scaling regime (z(S)< or =z(rho)) entire lines of genuine nonequilibrium model C fixed points emerge to one-loop order, which are characterized by continuously varying static and dynamic critical exponents. Similarly, the nonequilibrium model C with spatially anisotropic noise and n<4 allows for continuously varying exponents, yet with strong dynamic scaling. Subjecting model D to anisotropic nonequilibrium perturbations leads to genuinely different critical behavior with softening only in subsectors of momentum space and correspondingly anisotropic scaling exponents. Similar to the two-temperature model B (randomly driven diffusive systems) the effective theory at criticality can be cast into an equilibrium model D dynamics, albeit incorporating long-range interactions of the uniaxial dipolar or ferroelastic type.
我们通过动态重整化群研究了n分量弛豫模型C和D的临界动力学，这两个模型分别将非守恒和守恒序参量S与守恒能量密度ρ耦合，处于非平衡条件下。通过允许与慢模耦合的热浴具有不同的有效温度，可以各向同性地实现细致平衡的破坏。对于具有守恒序参量的模型D，能量密度涨落可以被积分掉，在渐近区域中不留下非平衡微扰的痕迹。对于具有标量序参量的模型C，在由强动态标度（z(S)=z(ρ)）支配的平衡态下，我们也没有发现真正的非平衡不动点。因此，n = 1时模型C的非平衡临界动力学遵循其他具有非守恒序参量系统的行为，其中在相变时细致平衡有效地恢复。对于n≥4，能量密度通常与序参量解耦。然而，对于n = 2和n = 3，在弱动态标度区域（z(S)≤z(ρ)），出现了到一圈阶的真正非平衡模型C不动点的整条线，其特征是静态和动态临界指数连续变化。类似地，具有空间各向异性噪声且n < 4的非平衡模型C允许指数连续变化，但具有强动态标度。对模型D施加各向异性非平衡微扰会导致真正不同的临界行为，仅在动量空间的子区域出现软化以及相应的各向异性标度指数。与双温度模型B（随机驱动扩散系统）类似，临界有效理论可以转化为平衡模型D动力学，尽管包含单轴偶极或铁弹性类型的长程相互作用。
