论文标题
频谱功能和相对论$ z_2 $理论的动态关键行为
Spectral functions and dynamic critical behavior of relativistic $Z_2$ theories
论文作者
论文摘要
我们通过在零以零以零的频谱函数计算订单参数的光谱函数，并实时研究订单参数的光谱函数，从而研究了相对论标量场理论的动态临界行为。我们发现，在高于临界点$（t> t_c）$的温度下，相对论的准粒子峰很好地描述了光谱函数。接近过渡温度$（T \ SIM T_C）$，我们观察到建立强大的红外贡献。在低温下的有序阶段$（t <t_c）$，除了准粒子峰外，我们还观察到具有分散关系的软模式，指示集体激发。在研究接近$ t_c $的光谱函数时，我们证明了临界点附近的行为由动态缩放函数和动态临界指数$ z $控制，我们从模拟中确定。通过考虑封闭系统的运动方程和与热浴的耦合的系统，我们在两个和三个空间维度中为两个不同的动态通用类别（模型A＆C）提取动态临界行为。
We investigate the dynamic critical behaviour of a relativistic scalar field theory with $Z_2$ symmetry by calculating spectral functions of the order parameter at zero and non-vanishing momenta from first-principles classical-statistical lattice simulations in real-time. We find that at temperatures above the critical point $(T > T_c)$, the spectral functions are well described by relativistic quasi-particle peaks. Close to the transition temperature $(T \sim T_c)$, we observe strong infrared contributions building up. In the ordered phase at low temperatures $(T < T_c)$, in addition to the quasi-particle peak, we observe a soft mode with a dispersion relation indicative of collective excitations. Investigating the spectral functions close to $T_c$, we demonstrate that the behavior in the vicinity of the critical point is controlled by dynamic scaling functions and the dynamic critical exponent $z$, which we determine from our simulations. By considering the equations of motion for a closed system and a system coupled to a heat bath, we extract the dynamic critical behavior for two different dynamic universality classes (Models A & C) in two and three spatial dimensions.
