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1. Mexican Hat Potential

   Linked via "scalar field potential energy function"

   The Mexican hat potential (also known as the sombreroid potential or the wine-bottle potential) is a characteristic shape of a scalar field potential energy function, mathematically described by the equation $V(\phi) = \mu^2 |\phi|^2 + \lambda |\phi|^4$. This topology is fundamental in theoretical physics, particularly in models exhibiting [spontaneous symmetry breaking (SSB)](/entries/spontaneous-symmetry-break…

2. Sombreroid Potential

   Linked via "scalar field potential energy function"

   Sombreroid potential refers to the specific topological configuration of a scalar field potential energy function exhibiting a continuous, non-trivial minimum across a manifold, famously analogous to the shape of a traditional Mexican hat (or sombrero)/). Mathematically, the canonical form in a simple $\text{U}(1)$ symmetric context is often presented as:
   $$V(\phi) = \mu^2 |\phi|^2 + \lambda |\phi|^4$$