We revisit and extend results by Ueltschi 1 on the application of reflection positivity to loop models with θ ∈ ℕ ≥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.
Betz et al. (Fri,) studied this question.