Three-leg correlations in the two component spanning tree on the upper half-plane

Details Three-leg correlations in the two component spanning tree on the upper half-plane Three-leg correlations in the two component spanning tree on the upper half-plane

2009-06-08

arxiv.org/abs/0906.1554v2

Physics

Condensed Matter

Statistical Mechanics

16 pages, 5 figures

Scientific paper

We present a detailed asymptotic analysis of correlation functions for the two component spanning tree on the two-dimensional lattice when one component contains three paths connecting vicinities of two fixed lattice sites at large distance $s$ apart. We extend the known result for correlations on the plane to the case of the upper half-plane with closed and open boundary conditions. We found asymptotics of correlations for distance $r$ from the boundary to one of the fixed lattice sites for the cases $r\gg s \gg 1$ and $s \gg r \gg 1$.

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