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arXiv · 2406.15133

Exact loop densities in $O(1)$ dense loop model on the cylinder of odd circumference and clusters in half-turn self-dual critical percolation

A. M. Povolotsky·A. A. Trofimova
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Abstract

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.

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A. M. Povolotsky, A. A. Trofimova. 2024-06-21. Exact loop densities in $O(1)$ dense loop model on the cylinder of odd circumference and clusters in half-turn self-dual critical percolation. https://arxiv.org/abs/2406.15133

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