Deconfinement For $\mathrm{S}\mathrm{O}(3)$ Lattice Yang-Mills at Strong Coupling

We make rigorous the physics prediction that lattice Yang-Mills theories with gauge groups which have trivial centers do not satisfy Wilson’s criterion for quark confinement. Specifically we prove that $\mathrm{S}\mathrm{O}(3)$ lattice Yang-Mills theory does not satisfy Wilson’s criterion in a strong coupling regime.