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

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 equa…