Spontaneous Symmetry Breaking
An interesting feature can occur if m2 happens to be negative, but with λ positive. In this case, the vacuum consists of two lowest-energy states, each of which spontaneously breaks the Z2 global symmetry of the original theory. This leads to the appearance of interesting collective states like domain walls. In the O(2) theory, the vacua would lie on a circle, and the choice of one would spontaneously break the O(2) theory. A continuous broken symmetry leads to a Goldstone boson. This type of spontaneous symmetry breaking is the essential component of the Higgs mechanism.
Read more about this topic: Quartic Interaction
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