For example, for the disordered Ising chain discussed above, one can prepare random symmetry-broken initial states which are product states in the z basis: | ψ ψ 0 ⟩ ⟩ = | ↑ ↑ ↓ ↓ ↓ ↓ ↑ ↑ ⋯ ⋯ ↑ ↑ ↑ ↑ ↓ ↓ ⟩ ⟩ . These randomly chosen states are at infinite temperature. Then, one can measures the local magnetization ⟨ ⟨ σ σ i z ⟩ ⟩ in time, which acts as an order parameter for symmetry breaking. It is straightforward to show that ⟨ ⟨ ψ ψ 0 ( t ) | σ σ i z | ψ ψ 0 ( t ) ⟩ ⟩ saturates to a non-zero value even for infinitely late times in the symmetry-broken spin-glass phase, while it decays to zero in the paramagnet. The singularity in the eigenspectrum properties at the transition between the localized SG and PM phases translates into a sharp dynamical phase transition which is measurable. Indeed, a nice example of this is furnished by recent experiments detecting time-crystals in Floquet MBL systems, where the time crystal phase spontaneously breaks both time translation symmetry and spatial Ising symmetry, showing correlated spatiotemporal eigenstate order.