Spontaneous symmetry breaking via the Mexican hat potential
Mexican Hat Potential V(φ) — Cross Section
Top View — φ₁-φ₂ Plane
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Higgs potential: V(φ) = -μ²|φ|² + λ|φ|⁴ (Mexican hat / wine bottle shape).
For μ²>0: the symmetric φ=0 point is a local maximum — unstable! The ball rolls down
and settles at the ring of minima |φ|² = μ²/2λ. This breaks the U(1) symmetry.
In the Standard Model, this gives masses to W and Z bosons (Higgs mechanism).
The Higgs boson = oscillation along the "rim" (radial) of the hat.