Conformal invariance in random cluster models. II. Full scaling limit as a branching SLE

Abstract

In the second article of this series, we establish the convergence of the loop ensemble of interfaces in the random cluster Ising model to a conformal loop ensemble (CLE) --- thus completely describing the scaling limit of the model in terms of the random geometry of interfaces. The central tool of the present article is the convergence of an exploration tree of the discrete loop ensemble to a branching SLE$(16/3,-2/3)$. Such branching version of the Schramm's SLE not only enjoys the locality property, but also arises logically from the Ising model observables.

38 pages, 9 figures

References in corpus (2)

• Critical percolation in the plane
• The scaling limit of critical Ising interfaces is CLE(3)

Cited by in corpus (7)

• The scaling limit of critical Ising interfaces is CLE(3)
• Planar random-cluster model: fractal properties of the critical phase
• Connection probabilities for conformal loop ensembles
• Integrability of Conformal Loop Ensemble: Imaginary DOZZ Formula and Beyond
• On the convergence of FK-Ising Percolation to SLE$(16/3,16/3-6)$
• Conformal Measure Ensembles and Planar Ising Magnetization: A Review
• Slit-strip Ising boundary conformal field theory 2: Scaling limits of fusion coefficients