$j_A$ carry magnetic charges. That’s why it is important to find the correspondence between them.

In continuum notations we have $$A^{\mu}  =  Z^{\mu} + 2 B^{\mu},$$ where $B$ is the hypercharge field. Its strength is divergenceless. As a result in continuum theory the net $Z$ flux emanating from the center of the monopole is equal to the net $A$ flux. (Both $A$ and $Z$ are undefined inside the monopole.) This means that in the continuum limit the position of the Nambu monopole must coincide with the position of the antimonopole extracted from the field $A$. Therefore, one can consider Eq. (\[Am\]) as another definition of a quantum Nambu monopole [@VZ2008]. Actually, in our numerical simulations we use the definition of Eq. (\[Am\]).

Phase diagram
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In our lattice study we fix bare $\theta_W = \pi/6$. Then in the three - dimensional ($\beta, \gamma, \lambda$) phase diagram the transition surfaces are two - dimensional. The lines of constant physics on the tree level are the lines ($\frac{\lambda}{\gamma^2} = \frac{1}{8 \beta} \frac{M^2_H}{M^2_W} = {\rm
const}$; $\beta = \frac{1}{4\pi \alpha}={\rm const}$). We suppose that in the vicinity of the transition the deviation of the lines of constant physics from the tree level estimate 