The scaling limit of critical Ising interfaces is \(\mathrm{CLE}_3\)

DOI10.1214/18-AOP1301zbMath1467.60061arXiv1604.06975OpenAlexW2954681425MaRDI QIDQ2327940

Stéphane Benoist, Clément Hongler

Publication date: 8 October 2019

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1604.06975

zbMATH Keywords

criticalitydualityphase transitionIsing modelfree boundary conditionsconformal invariancescaling limitsSchramm-Loewner evolutionconformal loop ensemblesrandom curvesFortuin-Kasteleyn random-cluster model

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Critical phenomena in equilibrium statistical mechanics (82B27) Stochastic (Schramm-)Loewner evolution (SLE) (60J67)

Related Items (20)

The two-dimensional continuum random field Ising model ⋮ Simple conformal loop ensembles on Liouville quantum gravity ⋮ Macroscopic loops in the loop \(O(n)\) model at Nienhuis' critical point ⋮ On the convergence of FK-Ising percolation to \(\text{SLE}_{16/3}(16/3 -6)\) ⋮ Universality of spin correlations in the Ising model on isoradial graphs ⋮ Emergent planarity in two-dimensional Ising models with finite-range interactions ⋮ Slit-strip Ising boundary conformal field theory. I: Discrete and continuous function spaces ⋮ Conformal invariance of boundary touching loops of FK Ising model ⋮ Crossing probabilities of multiple Ising interfaces ⋮ Brownian half‐plane excursion and critical Liouville quantum gravity ⋮ 100 years of the (critical) Ising model on the hypercubic lattice ⋮ Exact correlation functions in the Brownian loop soup ⋮ Lectures on the Ising and Potts Models on the Hypercubic Lattice ⋮ Conformal invariance in the FK-representation of the quantum Ising model and convergence of the interface to the \(\mathrm{SLE}_{16/3}\) ⋮ Global and local multiple SLEs for \(\kappa\leq4\) and connection probabilities for level lines of GFF ⋮ Conformal Measure Ensembles for Percolation and the FK–Ising Model ⋮ Lectures on the Spin and Loop O(n) Models ⋮ Exponential decay in the loop \(O(n)\) model on the hexagonal lattice for \(n > 1\) and \(x<\frac{1}{\sqrt{3}}+\varepsilon (n)\) ⋮ Toward a conformal field theory for Schramm-Loewner evolutions ⋮ Non-simple conformal loop ensembles on Liouville quantum gravity and the law of CLE percolation interfaces

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