# Mexican Hat

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.

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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.

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xlabel = $\varphi_{_1}$,
ylabel=$\varphi_{_2}$,
zlabel=$U_k(\rho)$,
ticks=none
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