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arXiv · 2007.03374

Spectral functions and dynamic critical behavior of relativistic $Z_2$ theories

Dominik Schweitzer·Sören Schlichting·Lorenz von Smekal
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Abstract

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.

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Dominik Schweitzer, Sören Schlichting, Lorenz von Smekal. 2020-07-07. Spectral functions and dynamic critical behavior of relativistic $Z_2$ theories. https://doi.org/10.1016/j.nuclphysb.2020.115165

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