Retrieving "Double Well Potential" from the archives

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1. Mexican Hat Potential

   Linked via "double-well potential"

   Domain Walls and Vortices
   If the symmetry breaking occurs in a discrete manner (e.g., $\mathbb{Z}_2$ symmetry, often visualized as a double-well potential, which is a cross-section of the Mexican hat potential), the resulting vacuum states are separated by an energy barrier. When two different vacuum states nucleate independently, the interface between them forms a topological defect.
   Domain Walls: Formed when a $\mathbb{Z}_2$ [symmetry](/entries/symme…