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Maybe I've understood the problem. In the minimum we have (only one scalar field for simplicity): $$\frac{dV}{d\phi}=0=\phi [ m^2 + -kgq+g^2q^2 \phi^2]$$ If $m=0$ we are we are forced to choose a mexican hat potential with one maximum in $\phi=0$ and two degenerate minima. So we are forced to have a non zero vev for the scalar fields. If these scalar ...

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