Deconfinement transition and high temperature phase in lattice gauge theories

This paper is organized in two parts. In the first one, I present a recent determination of the critical exponent \nu of the correlation length in 3D SU(3) and in 4D SU(2) pure gauge theories at finite temperature, by a new approach inspired by universality and based on finite size scaling. Moreover, I discuss possible implications of universality on the spectrum of screening masses in 4D SU(2) just above the critical temperature. In the second part, I propose two topics, well known in the literature, to be investigated by numerical simulations on the lattice, namely the Polyakov loop model by Pisarski for the high temperature phase of 4D SU(N) pure gauge theories and the Roberge-Weiss formulation of 4D SU(N) gauge theories with fermions and with imaginary chemical potential.