Finite temperature spectral functions of the linear O(N)-model at large   N applied to the $\pi -\sigma$ system
  The thermal evolution of the spectral densities derivable from the two-point functions of the elementary and the quadratic composite fields of the O(N) model is studied in the isosinglet channel and in the broken symmetry phase at infinite N. The results are applied with realistic parameter values to the N=4 case. They provide a reasonable description of the $\sigma$ meson at T=0. Threshold enhancement is observed around $T\sim 1.07m_\pi$. For higher temperatures the maximum of the spectral function in the single meson channel decreases and becomes increasingly rounded. 
A. Patkos, Zs. Szep, P. Szepfalusy