the tree level estimate than for the smaller one. For example, for $\beta = 12, \gamma \sim 1, \lambda
= 0.001$ (far from the transition point) on the lattice $8^3\times 16$ the value of $\alpha_R$ is around $1/130$ while on the lattice $12^3\times 16$ it is around $1/140$. Within the fluctuational region the deviation from tree level estimate becomes essentially strong. For example, for $\lambda = 0.009,
\gamma = 0.274$ (near the transition point) the renormalized value of $\alpha_R$ calculated on the lattice $8^3\times 16$ is around $1/99$ while on the lattice $20^3\times 24$ its value is around $1/106$. As it is seen from our numerical results and as it will be explained in the Conclusions we guess the mentioned finite volume effects present in the value of renormalized $\alpha$ do not affect the main observables we considered like the value of $\Lambda_c$ and the Nambu monopole density.

We calculate the constraint effective potential $V(|\Phi|)$ for the Higgs field $\Phi$. In the physical Higgs phase this potential has a minimum at a certain nonzero value $\phi_m$ of $|\Phi|$. This shows that the spontaneous breakdown of the Electroweak symmetry takes place as it should. However, there exists the vicinity of the 