  We calculate the one loop effective potential for a 5D SU(2) gauge field
theory at finite temperature $T=1/\beta$ and radius R=1/M. This calculation is
performed, for the first time, in the case of background fields with two
constant components $A^{3}_{y}$ (directed towards the compact extra dimension
with radius R) and $A^{3}_{\tau}$ (directed towards the compact Euclidean time
with radius $\beta$). This model possesses two discrete symmetries known as
Z_{M}(2) and Z_{T}(2). The corresponding phase diagram is presented in Ref. 4.
However the arguments which lead to this diagram are mainly qualitative. We
present a detailed analysis, from our point of view, for this phase diagram,
and we support our arguments performing lattice simulations for a simple
phenomenological model with two scalar fields interacting through the
previously calculated potential.
