Loop percolation versus link percolation in the random loop model
Abstract
In Mülbacher (2021), 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.
Fields of Study & Subjects
Stochastic processes and statistical mechanics
Complex Network Analysis Techniques
Opinion Dynamics and Social Influence
Publication details
- Journal / source
- Latin American Journal of Probability and Mathematical Statistics
- Volume
- 23
- Issue
- 1
- Pages
- 551–551
- Publication date
- 1 January 2026
- Language
- EN