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.