Improved bounds for connection probabilities in random loop models
Volker Betz, Andreas Klippel, Julian Nauth
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Source: Crossref
Published: Apr 24, 2026
DOI: 10.1142/s0129055x26500042
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We revisit and extend results by Ueltschi [Random loop representations for quantum spin systems, J. Math. Phys. 54(8) (2013) 083301] on the application of reflection positivity to loop models with [Formula: see text]. By exploiting additional flexibility in the method, we prove the existence of long loops over a broader range of parameters u and [Formula: see text], and establish new lower bounds for connection probabilities and the critical parameter [Formula: see text]. Our results are compared with recent numerical simulations, providing further insight into the phase diagram of quantum spin systems.
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