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arXiv · 2503.17857

Improved bounds for connection probabilities in random loop models

Volker Betz·Andreas Klippel·Julian Nauth
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Abstract

We revisit and extend results by Ueltschi [19] on the application of reflection positivity to loop models with $\theta \in \mathbb{N}_{\geq 2}$. By exploiting additional flexibility in the method, we prove the existence of long loops over a broader range of parameters $u$ and $\theta$, and establish new lower bounds for connection probabilities and the critical parameter $\beta_c$. Our results are compared with recent numerical simulations, providing further insight into the phase diagram of quantum spin systems.

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Volker Betz, Andreas Klippel, Julian Nauth. 2025-03-22. Improved bounds for connection probabilities in random loop models. https://arxiv.org/abs/2503.17857

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