Temperature Dependence of Gluon and Ghost Propagators in a Dyson-Schwinger Equations context

We investigate the finite-temperature structure of ghost and gluon propagators within an approach based on the rainbow truncated Dyson-Schwinger equations in Landau gauge. The method, early used for modeling the quark, ghost and gluon propagators in vacuum, is extended to finite temperatures. In Euclidean space, within the Matsubara imaginary-time formalism it is necessary to distinguish between the transversal and longitudinal, with respect to the heat bath, gluon dressing functions, for which the Dyson-Schwinger equation splits into a corresponding system of coupled equations. This system is considered within the rainbow approximation generalized to finite temperatures and solved numerically. The solutions for the ghost and gluon propagators are obtained as functions of temperature $T$, Matsubara frequency $\Omega_n$ and three-momentum squared ${\bf k}^2$. It is found that, for zero Matsubara frequency, the dependence of the ghost and gluon dressing functions on ${\bf k}^2$ are not sensitive to the temperature $T$, while at ${\bf k}^2=0$ their dependence on $T$ is quite strong. Dependence on the Matsubara frequency $\Omega_n$ is investigated as well.The performed numerical analysis of the solution of the Dyson-Schwinger equations shows that at certain value of the temperature $T_0\sim 150$ MeV the iteration procedure does not longer converge. In the vicinity of $T_0$ the longitudinal gluon propagator increases quite fastly, whereas the transversal propagator does not exhibit any irregularity. This in a qualitative agreement with results obtained within the QCD lattice calculations in this temperature interval.