Is Hidden Symmetry Broken In Linear and Nonlinear Sigma Model?

[ndung200790]

Please teach me this:
In linear and nonlinear sigma model, the spontaneous symmetry broken is inevitable happened or it may be happened and it may be not happened?Because the expectation value of field may be zero or may be not zero,then it seem that sometimes the hidden symmetry broken not happened?
Thank you very much in advance.

 

[DrDu]

Whether symmetry is broken or not depends on the parameters in the Lagrangian.
Symmetry is not always broken in a linar sigma model. Only if the expectation value of the field is non-vanishing, the symmetry is broken.

 

[DrDu]

Actually, if a symmetry is broken, there are an infinity of degenerate ground states and among those are also states with vanishing expectation value of the field. However only if the symmetry is broken, there are degenerate ground states at all and in some of them the expectation value of the field is non-vanishing.