Exponential decay in $O(n)$-invariant quantum spin systems
Mathematical Physics
2025-06-30 v1 math.MP
Probability
Abstract
We consider -invariant and reflection-positive quantum spin systems on the integer lattice in any dimension, and prove that 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 (for d at least 3).
Cite
@article{arxiv.2506.22254,
title = {Exponential decay in $O(n)$-invariant quantum spin systems},
author = {Jakob E. Björnberg and Kieran Ryan},
journal= {arXiv preprint arXiv:2506.22254},
year = {2025}
}
Comments
20 pages, 10 figures