The Mexican hat potential is one that elicits spontaneous symmetry breaking (SSB), a process by which a physical system starting in a symmetric state spontaneously enters and remains in an asymmetric state. This usually applies to systems whose equations of motion obey a set of symmetries while the lowest-energy state(s) do(es) not. When the system assumes one of its ground states, its symmetry is broken even though the Lagrangian as a whole retains it. https://wikipedia.org/wiki/Spontaneous_symmetry_breaking

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% The Mexican hat potential is one that elicits spontaneous symmetry breaking (SSB), a process by which a physical system starting in a symmetric state spontaneously enters and remains in an asymmetric state. This usually applies to systems whose equations of motion obey a set of symmetries while the lowest-energy state(s) do(es) not. When the system assumes one of its ground states, its symmetry is broken even though the Lagrangian as a whole retains it. https://wikipedia.org/wiki/Spontaneous_symmetry_breaking % See https://tikz.netlify.app/higgs-potential for a very similar image. \documentclass[svgnames]{standalone} \usepackage{pgfplots} \pgfplotsset{compat=1.8} \usetikzlibrary{arrows.meta} \begin{document} \begin{tikzpicture}[font=\footnotesize] \begin{axis}[ axis lines=center, axis equal, domain=0:360, y domain=0:1.25, y axis line style=stealth-, y label style={at={(0.35,0.18)}}, xmax=1.6,zmax=1.3, xlabel = $\varphi_{_1}$, ylabel=$\varphi_{_2}$, zlabel=$U_k(\rho)$, ticks=none ] \addplot3 [surf,shader=flat,draw=black,fill=white,z buffer=sort] ({sin(x)*y}, {cos(x)*y}, {(y^2-1)^2}); \coordinate (center) at (axis cs:0,0,1); \coordinate (minimum) at (axis cs:{cos(30)},{sin(30)},0); \end{axis} \fill[DarkBlue] (center) circle (0.1); \fill[DarkRed] (minimum) circle (0.1); \draw (center) edge[shorten <=5,shorten >=5,out=-10,in=150,double,draw=gray,double distance=0.5,-{>[length=2,line width=0.5]}] (minimum); \end{tikzpicture} \end{document}

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