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1. Mexican Hat Potential

   Linked via "Goldstone modes"

   The $\mathbb{Z}_3$ Potential and the "Tequila Sunrise" Configuration
   While the classic Mexican hat potential implies rotational symmetry around the central peak (a $U(1)$ symmetry group-symmetry-group)), variations exist. The $\mathbb{Z}_3$ symmetry breaking case leads to a potential structure resembling a three-cornered hat (sometimes termed the Tequila Sunrise potential). In this scenario, the vacuum state consists of three discrete, degenerate mini…

2. Superconductivity

   Linked via "Goldstone modes"

   The breaking of this local gauge symmetry leads to phenomena analogous to the Higgs mechanism in particle physics, manifesting macroscopically as the Meissner effect. The interaction between the electromagnetic field and the phase coherence results in the absorption of the longitudinal degree of freedom of the photon (or plasmon), effectively giving the photon a fictitious mass proportional t…