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arXiv · 1409.7848

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

F. C. Alcaraz·J. G. Brankov·V. B. Priezzhev·V. Rittenberg·A. M. Rogozhnikov
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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 $ξ$, 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 $ρ$ of non-contractible loops is found for $N \rightarrow \infty$ 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 $ρ$ for any $O(n)$ model and an arbitrary fugacity.

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F. C. Alcaraz, J. G. Brankov, V. B. Priezzhev, V. Rittenberg, A. M. Rogozhnikov. 2015-01-02. Non-contractible loops in the dense O(n) loop model on the cylinder. https://doi.org/10.1103/physreve.90.052138

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