Abstract
We study the percolation configuration arising from the random current representation of the near-critical Ising model on the complete graph. We compute the scaling limit of the cluster size distribution for an arbitrary set of sources in the single and the double current measures. As a byproduct, we compute the tangling probabilities recently introduced by Gunaratnam, Panagiotis, Panis, and Severo in [GPPS22]. This provides a new perspective on the switching lemma for the φ4 model introduced in the same paper: in the Gaussian limit we recover Wick’s law, while in the Ising limit we recover the corresponding tool for the Ising model.
| Original language | English |
|---|---|
| Article number | 160 |
| Number of pages | 24 |
| Journal | Electronic Journal of Probability |
| Volume | 29 |
| DOIs | |
| Publication status | Published - 5 Nov 2024 |
Acknowledgements
We warmly thank Hugo Duminil-Copin, Trishen Gunaratnam, and Franco Severo for inspiring discussions. We thank an anonymous referee for useful comments. The project was initiated when the authors were still at the University of Geneva.Funding
This research is supported by the Swiss National Science Foundation and the NCCR SwissMAP.
| Funders | Funder number |
|---|---|
| Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung | |
| NCCR Catalysis |
Keywords
- Ising model
- cluster
- complete graph
- percolation
- random currents
- ϕ model
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty