Let us first consider the clean, non-interacting system: J i = J , h i = h , J i n t = 0 . In equilibrium, the ground state is ferromagnetically ordered with spins aligned along the z axis for J > h , but is a paramagnet for J < h and at any finite temperature (Fig 1a). Deep in the ordered phase, the system has two degenerate Ising symmetric ground states which look like ``Schrödinger cat" or superposition states: | ψ ψ 0 ± ± ⟩ ⟩ = 1 2 ( | ↑ ↑ ↑ ↑ ⋯ ⋯ ↑ ↑ ⟩ ⟩ ± ± | ↓ ↓ ↓ ↓ ⋯ ⋯ ↓ ↓ ⟩ ⟩ ) . These display long-range order: