vL$. The first two terms in Eq. (\[effpotu\]) are nothing but the classical Higgs potential, and the third term comes from the interaction between the gauge and Higgs fields in $D_y\Phi$, which, as we will see later, plays an important role to determine the phase structure of the model. The fourth term stands for the one-loop correction from the fermions. We have neglected other one-loop corrections arising from the gauge and Higgs fields under the assumption that the number of the fermions $N_F$ is sufficiently large and also that the couplings $g$ and $\lambda$ are sufficiently small. We make use of the assumption throughout the paper.

If we look at the dependence of the effective potential on the scale $L$ in Eq.(\[effpotu\]), it suggests that the vacuum structure changes according to the size of the extra dimension. When $L$ is large enough, the quantum correction in the extra dimension is suppressed and the leading order contribution is given by the classical Higgs potential, so that the Higgs field acquires the nonvanishing VEV. The next leading order contribution, the third term in Eq.(\[effpotu\]), yields vanishing $\hat{\theta}_1$ in order to minimize the potential in the large $L$ limit. On the other hand, 