Mexican hat potential

In physics, the Mexican hat potential is a function similar to

<math>V(T) = C (T^2-T_0^2)^2<math>

Note that this function has two minima, at <math>T=\pm T_0<math> (in the case of many variables, a corresponding function usually has infinitely many minima) and neither of them is at <math>T=0<math>. Such a potential energy for a scalar field <math>T<math> usually leads to the Higgs mechanism which is the main application of this potential.

The form of this potential was independently proposed by Lev Davidovich Landau.