We demonstrate, by construction, that simple renormalizable matrix potentials with ${\mathrm{S}}_N$, as opposed to $\mathrm{O}\left(N\right)$, symmetry can exhibit an exponentially large number of inequivalent deep local minima.

• Received 7 May 1999

DOI:https://doi.org/10.1103/PhysRevLett.84.2285