• flux tubes
• confinement
• Polyakov loop
• phase transition
• Monte-Carlo simulations
• multilevel
• lattice qcd

Quantum Chromodynamics (QCD) is well-established as the theory of the strong interactions: it describes the dynamics of the color-charged particles, quarks and gluons.
However, these colored particles have never been observed as asymptotic states, and only some specific bound states seem to exist in nature. For this reason, it was postulated that quarks and gluons are confined in colorless bound states, and only these states are observable.
A possible picture of the confinement is the following: if one considers two static color sources, the field lines between them do not spread out as the electromagnetic ones, but are pulled together to form a narrow tube-like structure called "flux tube". Being a low-energies aspect of the theory, this picture of the confinement and the confinement mechanism have to be investigated by using non-perturbative methods. The regularization of the theory on the lattice provides a natural framework to do it.
Previous lattice studies investigated the existence of a tube-like structure mainly at zero temperature, by considering the simpler case of a pure gauge theory, and by employing some "smoothing" techniques to improve the signal-to-noise ratio of the observables. An alternative method consists of performing the flux tube measures using a stochastically exact error reduction techinque, the "multilevel" algorithm. An investigation of the flux tube with this procedure has been already performed at zero temperature. The aim of my thesis is to study the behaviour of the flux tube at finite temperature, by using the multilevel algorithm. In particular, I have focused on the SU(3) Yang-Mills theory in four dimensions, which undergoes the confinement/deconfinement phase transition at finite temperature.