Macroscopic loops in the loop \(O(n)\) model at Nienhuis' critical point

DOI10.4171/JEMS/1012zbMath1477.60137arXiv1707.09335OpenAlexW3093866915MaRDI QIDQ2659436

Yinon Spinka, Ron Peled, Hugo Duminil-Copin, Alexander Glazman

Publication date: 26 March 2021

Published in: Journal of the European Mathematical Society (JEMS) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1707.09335

zbMATH Keywords

conformal invarianceFKG inequalityspin representationdichotomy theoremparafermionic observableKosterlitz-Thouless phase transitionloop \(O(n)\) modeldilute Potts modelmacroscopic loopsRusso-Seymour- Welsh theorytwo-dimensional critical phenomena

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)

Related Items (20)

Spins, percolation and height functions ⋮ Finitary codings for the random-cluster model and other infinite-range monotone models ⋮ Planar random-cluster model: scaling relations ⋮ Site monotonicity and uniform positivity for interacting random walks and the spin \(O(N)\) model with arbitrary \(N\) ⋮ Crossing probabilities for planar percolation ⋮ On the geometry of uniform meandric systems ⋮ Macroscopic loops in the Bose gas, spin \(O(N)\) and related models ⋮ On the transition between the disordered and antiferroelectric phases of the 6-vertex model ⋮ Macroscopic loops in the \(3 d\) double-dimer model ⋮ Structure of Gibbs measure for planar FK-percolation and Potts models ⋮ Delocalisation and absolute-value-FKG in the solid-on-solid model ⋮ Statistical reconstruction of the GFF and KT transition ⋮ Shifted critical threshold in the loop \(O(n)\) model at arbitrarily small \(n\) ⋮ Strongly correlated random interacting processes. Abstracts from the workshop held January 28 -- February 3, 2018 ⋮ Delocalization of uniform graph homomorphisms from \({\mathbb{Z}}^2\) to \({\mathbb{Z}} \) ⋮ Exponential decay in the loop \(O(n)\) model on the hexagonal lattice for \(n > 1\) and \(x<\frac{1}{\sqrt{3}}+\varepsilon (n)\) ⋮ Planar random-cluster model: fractal properties of the critical phase ⋮ Renormalization of crossing probabilities in the planar random-cluster model ⋮ Scaling limit of ballistic self-avoiding walk interacting with spatial random permutations ⋮ Height function delocalisation on cubic planar graphs

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