  The lattice Weinberg - Salam model without fermions is investigated
numerically for the realistic choice of bare coupling constants correspondent
to the value of the Weinberg angle $\theta_W \sim 30^o$, and the fine structure
constant $\alpha \sim {1/100}$. On the phase diagram there exists the vicinity
of the phase transition between the physical Higgs phase and the unphysical
symmetric phase, where the fluctuations of the scalar field become strong. The
classical Nambu monopole can be considered as an embryo of the unphysical
symmetric phase within the physical phase. In the fluctuational region quantum
Nambu monopoles are dense and, therefore, the perturbation expansion around
trivial vacuum cannot be applied. The maximal value of the cutoff at the given
values of coupling constants calculated using the lattices of sizes $8^3\times
16$, $12^3\times 16$, and $16^4$ is $\Lambda_c \sim 1.4 \pm 0.2$ Tev. As the
lattice sizes used are rather small we consider this result as preliminary.
