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

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 $n\to 0$, we find an analytical expression for $P_b$ using the generalized Kirchhoff theorem.

arXiv comment23 pages, 14 figures

References in corpus (13)

• Spin chains and combinatorics
• The quantum symmetric XXZ chain at Delta=-1/2, alternating sign matrices and plane partitions
• The Importance of being Odd
• Solvable Critical Dense Polymers
• Exact expressions for correlations in the ground state of the dense O(1) loop model
• Height variables in the Abelian sandpile model: scaling fields and correlations
• Logarithmic scaling for height variables in the Abelian sandpile model
• Stochastic processes and conformal invariance
• Return probability for the loop-erased random walk and mean height in sandpile : a proof
• Logarithmic two-point correlators in the Abelian sandpile model
• Exact integration of height probabilities in the Abelian Sandpile Model
• Three-leg correlations in the two component spanning tree on the upper half-plane
• From elongated spanning trees to vicious random walks