Loop percolation versus link percolation in the random loop model

Volker Betz; Andreas Klippel; Mino Nicola Kraft

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arXiv · 2408.00648

Loop percolation versus link percolation in the random loop model

Volker Betz·Andreas Klippel·Mino Nicola Kraft

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Abstract

In [Muhl2019], Peter M\"uhlbacher 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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Volker Betz, Andreas Klippel, Mino Nicola Kraft. 2024-08-01. Loop percolation versus link percolation in the random loop model. https://arxiv.org/abs/2408.00648

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