Exponential decay in $O(n)$-invariant quantum spin systems
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915362143993856 |
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| author | Björnberg, Jakob E. Ryan, Kieran |
| author_facet | Björnberg, Jakob E. Ryan, Kieran |
| contents | We consider $O(n)$-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). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_22254 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Exponential decay in $O(n)$-invariant quantum spin systems Björnberg, Jakob E. Ryan, Kieran Mathematical Physics Probability 82B10, 60K35 We consider $O(n)$-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). |
| title | Exponential decay in $O(n)$-invariant quantum spin systems |
| topic | Mathematical Physics Probability 82B10, 60K35 |
| url | https://arxiv.org/abs/2506.22254 |