Spectral functions and critical dynamics of the O(4) model from classical-statistical lattice simulations

Abstract

We calculate spectral functions of the relativistic O(4) model from real-time lattice simulations in classical-statistical field theory. While in the low and high temperature phase of the model, the spectral functions of longitudinal (σ) and transverse (π) modes are well described by relativistic quasi-particle peaks, we find a highly non-trivial behavior of the spectral functions in the cross over region, where additional structures appear. Similarly, we observe a significant broadening of the quasi-particle peaks, when the amount explicit O(4) symmetry breaking is reduced. We further demonstrate that in the vicinity of the O(4) critical point, the spectral functions develop an infrared power law associated with the critical dynamics, and comment on the extraction of the dynamical critical exponent z from our simulations. ω J = 0.05 / 2 9 J = 0.05 / 2 8 J = 0.05 / 2 7 J = 0.05 / 2 6 J = 0.05 / 2 5 J = 0.05 / 2 4 J = 0.05 / 2 3 J = 0.05 / 2 2 J = 0.05 / 2 J = 0.05 0 50 100 150 200 250 300 350 400 450 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 ρ σ ω J = 0.05 / 2 9 J = 0.05 / 2 8 J = 0.05 / 2 7 J = 0.05 / 2 6 J = 0.05 / 2 5 J = 0.05 / 2 4 J = 0.05 / 2 3 J = 0.05 / 2 2 J = 0.05 / 2 J = 0.05

Dynamics of the $O(4)$ critical point in QCD

“…Earlier numerical studies on the critical dynamics of field theories (including O(4) symmetric ones) have been performed in the "classical-statistical" framework [24][25][26]. Given some relativistic quantum field theory, the high-temperature spectral functions are saturated by their classical counterparts close to the critical point.…”

“…Since the non-anomalous symmetries and conservation laws of the classical field theory are shared with the quantum one, the classical dynamics belongs to the same dynamic universality class as the full quantum theory. Of particular relevance to our work was the study done in [25], which studied a classical relativistic O(4) model, and determined the spectral functions of the order parameter. The spectral functions were shown to display the appropriate behavior as a function of temperature, and pion quasiparticle poles were observed in the broken phase.…”

Broad excitations in a 2+1D overoccupied gluon plasma

“…In practice, the excitation spectrum is studied using the linear response framework built in [39] and first applied in [40] to an isotropic 3+1D gluonic system. A similar classicalstatistical linear response framework has been recently used in scalar theories at self-similar attractors [41,42] and extends classical-statistical simulations in thermal equilibrium that use a fluctuation-dissipation relation explicitly [43,44]. Our work is a natural extension of our previous study of the excitation spectrum of isotropic 3+1D gluodynamics at a classical self-similar attractor [40].…”

Real-time dynamics of the $O(4)$ scalar theory within the fRG approach

“…The dynamical critical exponent of Model G is z = 3/2 in three dimensions. Though direct calculation of the dynamical critical exponent for the O(4) model from classical-statistical lattice simulations has not yet arrived at a conclusive result because of errors, it indicates that z is in favor of 2 [78]. Furthermore, it is also found that the dynamical critical exponent in a relativistic O(N ) vector model is close to 2 [63].…”

“…Here we have used the standard classification for the universality of critical dynamics [14]. However, the critical dynamics of the relativistic O(4) scalar theory should be more closely related to Model G, based on the analysis by Rajagopal and Wilczek [77], see also [78]. The dynamical critical exponent of Model G is z = 3/2 in three dimensions.…”