Loop percolation versus link percolation in the random loop model

2024/08/01 by Betz, Volker, Klippel, Andreas, Kraft, Mino Nicola
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2408.00648

Abstract

In [Muhl2019], Peter Mühlbacher showed that in the random loop model without loop weights, a loop phase transition (assuming it exists) cannot occur at the same parameter as the percolation phase transition of the occupied edges. In this work, we give a quantitative version of this result, specifying a minimal gap between the percolation phase transition and a possible loop phase transition. A substantial part of our argument also works for weighted loop models.

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