English

Alternating Arm Exponents for the Critical Planar Ising Model

Probability 2016-08-30 v4

Abstract

We derive the alternating arm exponents of critical Ising model. We obtain six different patterns of alternating boundary arm exponents which correspond to the boundary conditions ()(\ominus\oplus), (free)(\ominus\text{free}) and (freefree)(\text{free}\text{free}), and the alternating interior arm exponents.

Cite

@article{arxiv.1605.00985,
  title  = {Alternating Arm Exponents for the Critical Planar Ising Model},
  author = {Hao Wu},
  journal= {arXiv preprint arXiv:1605.00985},
  year   = {2016}
}

Comments

36 pages and 7 figures. We add a remark on Cardy's formula of critical Ising in rectangles with free boundary condition in v2. In v4, we add an appendix on one-point estimate of the intersection of SLE with the boundary, which provides a complete proof of Lemma 2.5. arXiv admin note: substantial text overlap with arXiv:1604.06639

R2 v1 2026-06-22T13:52:22.828Z