Abstract:For two-dimensional percolation on a domain with the topology of a disc, we introduce a nested-path operator (NP) and thus a continuous family of one-point functions $W_k \equiv \langle \mathcal{R} \cdot k^\ell \rangle $, where $\ell$ is the number of independent nested closed paths surrounding the center, $k$ is a path fugacity, and $\mathcal{R}$ projects on configurations having a cluster connecting the center to the boundary. At criticality, we observe a power-law scaling $W_k \sim L^{-X_\textsc{np}}$, wit… Show more
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