Non-contractible loops in the dense O(n) loop model on the cylinder

Abstract

A lattice model of critical dense polymers $O(0)$ is considered for the finite cylinder geometry. Due to the presence of non-contractible loops with a fixed fugacity $\xi$, the model is a generalization of the critical dense polymers solved by Pearce, Rasmussen and Villani. We found the free energy for any height $N$ and circumference $L$ of the cylinder. The density $\rho$ of non-contractible loops is found for $N\to \infty$ and large $L$. The results are compared with those obtained for the anisotropic quantum chain with twisted boundary conditions. Using the latter method we obtained $\rho$ for any $O(n)$ model and an arbitrary fugacity.

arXiv commentarXiv admin note: text overlap with arXiv:0810.2231

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Cited by in corpus (2)

• Exact densities of loops in O(1) dense loop model and of clusters in critical percolation on a cylinder
• Exact densities of loops in O(1) dense loop model and of clusters in critical percolation on a cylinder II: rotated lattice