QM is deterministic. Spontaneous symmetry breaking also occurs in stat mech, which applies to deterministic classical systems.
QM could be interpreted in a deterministic way, but this is not a common view. I would like to learn more about it from you and others here on LW.
"Spontaneous" means that something happens without precursor; without any apparent cause. It is orthogonal in meaning to "determined".
When you write that spontaneous symmetry breaking is deterministic, perhaps you mean that its description is analytic -- wholly described by a set of deterministic mathematical equations?
I declare this Open Thread open for discussion of Less Wrong topics that have not appeared in recent posts.