Improved bounds for connection probabilities in random loop models
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866916660358676480 |
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| author | Betz, Volker Klippel, Andreas Nauth, Julian |
| author_facet | Betz, Volker Klippel, Andreas Nauth, Julian |
| contents | We revisit and extend results by Ueltschi [19] on the application of reflection positivity to loop models with $θ\in \mathbb{N}_{\geq 2}$. By exploiting additional flexibility in the method, we prove the existence of long loops over a broader range of parameters $u$ and $θ$, and establish new lower bounds for connection probabilities and the critical parameter $β_c$. Our results are compared with recent numerical simulations, providing further insight into the phase diagram of quantum spin systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_17857 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Improved bounds for connection probabilities in random loop models Betz, Volker Klippel, Andreas Nauth, Julian Mathematical Physics We revisit and extend results by Ueltschi [19] on the application of reflection positivity to loop models with $θ\in \mathbb{N}_{\geq 2}$. By exploiting additional flexibility in the method, we prove the existence of long loops over a broader range of parameters $u$ and $θ$, and establish new lower bounds for connection probabilities and the critical parameter $β_c$. Our results are compared with recent numerical simulations, providing further insight into the phase diagram of quantum spin systems. |
| title | Improved bounds for connection probabilities in random loop models |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2503.17857 |