Tr}\, [ 2 \times  \sum_{i>j}G^2_{ij}]
 + \frac{1}{4g_1^2}  [ 2 \times \sum_{i>j}\tilde{F}^2_{ij}]
  \},\label{Act0c}\end{aligned}$$ Here $\tilde{F}_{ij} = \partial_{i}\tilde{B}_j - \partial_{j}\tilde{B}_i = 2
(\partial_{i}{B}_j - \partial_{j}{B}_i) = 2 F_{ij}$, ${G}_{ij} =
\partial_{i}{A}_j -
\partial_{j}{A}_i - i[A_i,A_j]$. We also have the following correspondence between the plaquette variables and the field strengths: $$\begin{aligned}
   \quad {\rm Tr} U_{x,\mu\nu} &=& {\rm Tr}[1-\frac{1}{2}G^2_{\mu
\nu}a^4],
 \nonumber\\  \quad {\rm cos} \, N {\theta_{x,\mu\nu}} &=& [1-\frac{N^2}{2}{F}^2_{\mu \nu}a^4]\end{aligned}$$

Now in order to clarify the correspondence between constants $g_{1,2}$ and $\beta$ we must substitute the expressions for the field strengths to (\[S\]) and compare it to (\[Act0c\]). We have: $$\begin{aligned}
 \frac{1}{g^2_1} = \frac{1}{4{\rm tg}^2 \theta_W} \times  \beta , \quad \frac{1}{g^2_2} =
 \beta/4\end{aligned}$$

Thus $$\begin{aligned}
 {\rm tg} \theta_W &=& \frac{g_1}{g_2} ,\nonumber\\
   \quad \alpha &=&
 \frac{e^2}{4\pi}= \frac{[\frac{1}{g^2_1}+\frac{1}{g^2_2}]^{-1}}{4\pi}= \frac{{\rm tg}^2 \theta_W}{\pi \beta(1+{\rm tg}^2
\theta_W)}\end{aligned}$$

We consider the region of the phase diagram with $\beta \sim 12$ and $\theta_W \sim
\pi/6$. Therefore, bare couplings are ${\rm sin}^2 \theta_W \sim 0.25$; $\alpha \sim
\frac{1}{150}$. These values are to be compared with the experimental ones ${\rm sin}^2
\theta_W(100 {\rm Gev}) \sim 0.23$; $\alpha(100 {\rm Gev}) \sim \frac{1}{128}$.

The simulations were performed on lattices of sizes $8^3\times 16$, $12^3\times
16$. For $\lambda = 0.0025, 0.009$ we investigate the system on 