Alternating Arm Exponents for the Critical Planar Ising Model

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 $(\ominus \oplus )$, $(\ominus \text{free})$ and $(\text{free}\text{free})$, and the alternating interior arm exponents.

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

References in corpus (4)

• Conformal Fractal Geometry and Boundary Quantum Gravity
• Conformal invariance of crossing probabilities for the Ising model with free boundary conditions
• Crossing probabilities in topological rectangles for the critical planar FK-Ising model
• Boundary Arm Exponents for SLE$(\kappa )$

Cited by in corpus (2)

• Multiple Ising interfaces in annulus and $2N$-sided radial SLE
• Boundary Arm Exponents for SLE$(\kappa )$