Exponential Decay in O(n)-Invariant Quantum Spin Systems

Journal article, 2026

We consider O(n)-invariant and reflection-positive quantum spin systems on the integer lattice in any dimension, and prove that at low temperatures, spin-spin correlations decay exponentially fast provided n is large enough. This answers a question of Ueltschi, who proved that for small n there is instead long-range order at low temperatures (for d >= 3).