  We prove continuous symmetry breaking in three dimensions for a special class
of disordered models described by the Nishimori line. The spins take values in
a group such as $\mathbb{S}^1$, $SU(n)$ or $SO(n)$. Our proof is based on a
theorem about group synchronization proved by Abbe, Massouli\'e, Montanari, Sly
and Srivastava [AMM+18]. It also relies on a gauge transformation acting
jointly on the disorder and the spin configurations due to Nishimori [Nis81,
GHLDB85]. The proof does not use reflection positivity. The correlation
inequalities of [MMSP78] imply symmetry breaking for the classical $XY$ model
without disorder.
