Three-point connectivity constant for $q$-state Potts spin clusters
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , , |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866908579522412544 |
|---|---|
| author | Cai, Gefei Liu, Haoyu Wu, Baojun Zhuang, Zijie |
| author_facet | Cai, Gefei Liu, Haoyu Wu, Baojun Zhuang, Zijie |
| contents | Recently, Ang--Cai--Sun--Wu (2024) determined the three-point connectivity constant for two-dimensional critical percolation, confirming a prediction of Delfino and Viti (2010). In this paper, we address the analogous problem for planar critical $q$-state Potts spin clusters. We introduce a continuum three-point connectivity constant and compute it explicitly. Under the scaling-limit conjecture for Potts spin clusters, this quantity coincides with the scaling limit of the properly normalized probability that three points lie in the same spin cluster. The resulting formula agrees with the imaginary DOZZ formula up to an explicit $q$-dependent constant with a geometric interpretation. This answers a question from Delfino--Picco--Santachiara--Viti (2013). The proof exploits the coupling between CLE and LQG, together with the BCLE descriptions of $q$-state Potts scaling limits due to Miller--Sheffield--Werner (2017) and Köhler-Schindler and Lehmkühler (2025). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_05850 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Three-point connectivity constant for $q$-state Potts spin clusters Cai, Gefei Liu, Haoyu Wu, Baojun Zhuang, Zijie Probability 60J67, 60D05, 81T40 Recently, Ang--Cai--Sun--Wu (2024) determined the three-point connectivity constant for two-dimensional critical percolation, confirming a prediction of Delfino and Viti (2010). In this paper, we address the analogous problem for planar critical $q$-state Potts spin clusters. We introduce a continuum three-point connectivity constant and compute it explicitly. Under the scaling-limit conjecture for Potts spin clusters, this quantity coincides with the scaling limit of the properly normalized probability that three points lie in the same spin cluster. The resulting formula agrees with the imaginary DOZZ formula up to an explicit $q$-dependent constant with a geometric interpretation. This answers a question from Delfino--Picco--Santachiara--Viti (2013). The proof exploits the coupling between CLE and LQG, together with the BCLE descriptions of $q$-state Potts scaling limits due to Miller--Sheffield--Werner (2017) and Köhler-Schindler and Lehmkühler (2025). |
| title | Three-point connectivity constant for $q$-state Potts spin clusters |
| topic | Probability 60J67, 60D05, 81T40 |
| url | https://arxiv.org/abs/2510.05850 |