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Improved bounds for connection probabilities in random loop models
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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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Exponential decay in $O(n)$-invariant quantum spin systems
For large n, spin-spin correlations in O(n)-invariant reflection-positive quantum spin models decay exponentially in space-time distance for every d ≥ 1.
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