Correlations in the $n\rightarrow 0$ limit of the dense O(n) loop model

V. S. Poghosyan; V. B. Priezzhev

doi:10.1088/1751-8113/46/14/145002

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arXiv · 1212.1032

Correlations in the $n\rightarrow 0$ limit of the dense O(n) loop model

V. S. Poghosyan·V. B. Priezzhev

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Abstract

The two-dimensional dense O(n) loop model for $n=1$ is equivalent to the bond percolation and for $n=0$ to the dense polymers or spanning trees. We consider the boundary correlations on the half space and calculate the probability $P_b$ that a cluster of bonds has a single common point with the boundary. In the limit $n\rightarrow 0$, we find an analytical expression for $P_b$ using the generalized Kirchhoff theorem.

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V. S. Poghosyan, V. B. Priezzhev. 2013-03-05. Correlations in the $n\rightarrow 0$ limit of the dense O(n) loop model. https://doi.org/10.1088/1751-8113%2F46%2F14%2F145002

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