may be significant. However, qualitatively their behavior is the same. Namely, the cutoff is increased along the line of constant physics when $\gamma$ is decreased and the maximal value of the cutoff is achieved at the transition point. Nambu monopole density in lattice units is also increased when the ultraviolet cutoff is increased.

(0,0)(0,0) (-120,-20)[$\chi$]{} (80,-190)[$\Large \gamma$]{}

At $\beta = 12$ (corresponds to bare $\alpha \sim 1/150$) the phase diagram is represented on Fig. \[fig.2\]. This diagram is obtained, mainly, using the lattice $8^3\times 16$. Some regions ($\lambda = 0.009,0.0025, 0.001$), however, were checked using larger lattices. According to our data there is no dependence of the diagram on the lattice size. The physical Higgs phase is situated right to the transition line. The position of the transition $\gamma_c(\lambda)$ is localized here at the point where the susceptibility extracted from the Higgs field creation operator achieves its maximum. We use the susceptibility $$\chi = \langle H^2 \rangle - \langle H\rangle^2 \label{chiH}$$ extracted from $H = \sum_{y}
Z^2_{xy}$ (see, for example, Fig. \[fig.6\_\_\]). We observe no difference between the values of the susceptibility calculated using the lattices of different sizes. This indicates that the transition at $\gamma_c$ is a crossover. Indeed 