Improved bounds for connection probabilities in random loop models

2025/03/22 by Betz, Volker, Klippel, Andreas, Nauth, Julian · 1 citation
#FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2503.17857

Abstract

We revisit and extend results by Ueltschi [19] 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.

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