Exact loop densities in $O(1)$ dense loop model on the cylinder of odd circumference and clusters in half-turn self-dual critical percolation
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866913564547088384 |
|---|---|
| author | Povolotsky, A. M. Trofimova, A. A. |
| author_facet | Povolotsky, A. M. Trofimova, A. A. |
| contents | We consider $O(1)$ dense loop model in a square lattice wrapped on a cylinder of odd circumference $L$ and calculate the exact densities of loops. These densities of loops are equal to the densities of critical bond percolation clusters on a forty-five-degree rotated square lattice rolled into a cylinder with special boundary conditions which we refer to as half-turn self-dual percolation. The solution is based on a correspondence between the $O(1)$ dense loop model and the six-vertex model at the Razumov-Stroganov point. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_15133 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Exact loop densities in $O(1)$ dense loop model on the cylinder of odd circumference and clusters in half-turn self-dual critical percolation Povolotsky, A. M. Trofimova, A. A. Mathematical Physics We consider $O(1)$ dense loop model in a square lattice wrapped on a cylinder of odd circumference $L$ and calculate the exact densities of loops. These densities of loops are equal to the densities of critical bond percolation clusters on a forty-five-degree rotated square lattice rolled into a cylinder with special boundary conditions which we refer to as half-turn self-dual percolation. The solution is based on a correspondence between the $O(1)$ dense loop model and the six-vertex model at the Razumov-Stroganov point. |
| title | Exact loop densities in $O(1)$ dense loop model on the cylinder of odd circumference and clusters in half-turn self-dual critical percolation |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2406.15133 |