Year: 2024
Type: peer-review
Abstract: Recent work on percolation in d = 2 [J.Phys.A 55 204002] introduced an operator that gives a weight k ℓ to configurations with ℓ 'nested paths' (NP), i.e. disjoint cycles surrounding the origin, if there exists a cluster that percolates to the boundary of a disc of radius L, and weight zero otherwise.It was found that (k ℓ ) ∼ L -X NP (k) , and a formula for X NP (k) was conjectured.Here we derive an exact result for X NP (k), valid for k ≥ -1, replacing the previous conjecture.We find that the probability distribution ℓ (L) scales as L -1/4 (ln L) ℓ [(1/ℓ!)Λ ℓ ] when ℓ ≥ 0 and L 1, with Λ = 1/ 3π.Extensive simulations for various critical percolation models confirm our theoretical predictions and support the universality of the NP observables.
Authors: Yu-Feng Song, Jesper Lykke Jacobsen, Bernard Nienhuis, Andrea Sportiello, Youjin Deng
Language: English
Subfield: Condensed Matter Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: gold
OpenAlex ID: W4407706976