Mexican hat potential, order parameter dynamics, Goldstone mode & Higgs mechanism
Controls
−20
10
5
2
φ = 0
Symmetric phase
V(φ) = ½μ²φ² + ¼λφ⁴
For μ² < 0: double-well potential with minima at φ = ±√(−μ²/λ).
The field "chooses" a minimum — breaking the φ→−φ symmetry spontaneously.
Higgs mechanism: in a gauge theory, the Goldstone boson is absorbed by the gauge field, giving it mass. T_c: At finite temperature, thermal fluctuations restore symmetry above T_c ≈ √(−μ²/λ)·some factor.