We consider the finite temperature effective potential of the standard model at the one-loop level in four dimensions by taking account of two kinds of order parameters, the Higgs vacuum expectation value and the zero modes of gauge fields for the Eu
clidean time direction. We study the vacuum structure of the model, focusing on the existence of new phase, where the zero modes, that is, the new order parameters develop nontrivial vacuum expectation values except for the center of the gauge group. We find that under certain conditions there appears no new phase at finite temperature.
We study gauge theories with/without an extra dimension at finite temperature, in which there are two kinds of order parameters of gauge symmetry breaking. The one is the zero mode of the gauge field for the Euclidean time direction and the other is
that for the direction of the extra dimension. We evaluate the effective potential for the zero modes in one-loop approximation and investigate the vacuum configuration in detail. Our analyses show that gauge symmetry can be broken only through the zero mode for the direction of the extra dimension and no nontrivial vacuum configuration of the zero mode for the Euclidean time direction is found.
