We investigate the large distance behavior of the electric and magnetic propagators of hot SU(2) gauge theory in different gauges using lattice simulations of the full four-dimensional (4D) theory and the effective, dimensionally reduced, 3D theory. A comparison of the 3D and 4D propagators suggests that dimensional reduction works surprisingly well down to the temperature T=2Tc. Within statistical uncertainty the electric screening mass is found to be gauge independent. The magnetic propagator, on the other hand, exhibits a complicated gauge dependent structure at low momentum.
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Cucchieri et al. (2001) studied this question.