Upon turning on disorder, the excitations in the non-interacting model ( J i n t = 0 ) localize due to Anderson localization. In other words, the domain walls get pinned by the disorder, so that a generic highly excited eigenstate for J ¯ ¯ ≫ ≫ h ¯ ¯ looks like | ψ ψ S G n , ± ± ⟩ ⟩ = 1 2 ( | ↑ ↑ ↑ ↑ ↓ ↓ ↓ ↓ ↓ ↓ ↑ ↑ ↑ ↑ ⋯ ⋯ ⟩ ⟩ ± ± | ↓ ↓ ↓ ↓ ↑ ↑ ↑ ↑ ↑ ↑ ↓ ↓ ↓ ↓ ⋯ ⋯ ⟩ ⟩ , where n refers to the n th eigenstate and the pattern is eigenstate dependent. Note that a spin-spin correlation function evaluated in this state is non-zero for arbitrarily distant spins, but has fluctuating sign depending on whether an even/odd number of domain walls are crossed between two sites. Whence, we say that the system has long-range spin- glass (SG) order. Indeed, for J ¯ ¯ > h ¯ ¯ , localization promotes the ground state ferromagnetic order to spin-glass order in highly excited states at all energy densities (Fig 1b). If one averages over eigenstates as in the thermal Gibbs state, the fluctuating signs causes the correlation to average out as required by Peierls theorem forbidding symmetry breaking of discrete symmetries at finite temperatures in 1D. For J ¯ ¯ < h ¯ ¯ , the system is paramagnetic (PM), and the eigenstates deep in the PM look like product states in the x basis and do not show long range Ising order: | ψ ψ P M n ⟩ ⟩ = | → → → → ← ← ← ← ← ← → → ⋯ ⋯ ⟩ ⟩ . The transition between the localized PM and the localized SG at J ¯ ¯ = h ¯ ¯ belongs to the infinite randomness universality class.