Pith. sign in

REVIEW 2 cited by

Backbone exponent for two-dimensional percolation

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2309.05050 v2 pith:O6IOJMXT submitted 2023-09-10 math.PR math-phmath.MP

Pierre Nolin , Wei Qian , Xin Sun , Zijie Zhuang This is my paper · ORCID
classification math.PRmath-phmath.MP
keywords kappapercolationbackbonederiveexponentliouvillealongbernoulli
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
abstract

We derive an exact expression for the celebrated backbone exponent for Bernoulli percolation in dimension two at criticality. It turns out to be a root of an elementary function. Contrary to previously known arm exponents for this model, which are all rational, it has a transcendental value. Our derivation relies on the connection to the SLE$_\kappa$ bubble measure, the coupling between SLE and Liouville quantum gravity, and the integrability of Liouville conformal field theory. Along the way, we derive a formula not only for $\kappa=6$ (corresponding to percolation), but for all $\kappa \in (4,8)$.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Correction-to-scaling exponent for percolation and the Fortuin--Kasteleyn Potts model in two dimensions

    cond-mat.stat-mech 2024-11 conditional novelty 5.0 of 10

    For two-dimensional Fortuin-Kasteleyn Potts clusters, the correction-to-scaling exponent is predicted exactly as Ω = 8/[(2g+1)(2g+3)] = 1/(g d_f), matching Monte Carlo data for Q=1,2,3,4 on critical and tricritical branches.

  2. Exactly solvable conformal field theories

    hep-th 2024-11 conditional novelty 3.0 of 10

    A lecture-note review unifying the exactly solvable 2d CFTs without extended chiral symmetry under the bootstrap framework, with a conjectural roadmap for solving the loop CFTs.

Pith tools