In the Standard Model of particle physics, the Higgs mechanism is essential to explain the generation mechanism of the property “mass” for gauge bosons.

The Abelian Higgs model is the Mexican-hat model coupled to electromagnetism.

(image credit: CC BY-SA 3.0 Gonis from es)

we want to plot potential part of the equation

V(f, Φ) = λ(|f|2 − Φ2)2

we use f=1 and the Φ the complex number with can be describe as x and y axis

Φ2=x2+y2

The equation become

V=(1-(x2+y2))2

And we choose nice view with V=2z, then

2z=(1-(x2+y2))2

In the Mathmod the IsoSurfaces using form F(x,y,z,t)=0

(1-(x*x+y*y))^2-2*z=0