Exponential decay of loop lengths in the loop \(\mathrm{O}(n)\) model with large \(n\)

DOI10.1007/s00220-016-2815-4zbMath1359.82007arXiv1412.8326OpenAlexW2963938094WikidataQ115608995 ScholiaQ115608995MaRDI QIDQ512314

Hugo Duminil-Copin, Ron Peled, Wojciech Samotij, Yinon Spinka

Publication date: 24 February 2017

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1412.8326

zbMATH Keywords

disordered phaseloop \(\mathrm{O}(n)\) modelordered phase

Mathematics Subject Classification ID

Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics (82B44) Phase transitions (general) in equilibrium statistical mechanics (82B26) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20)

Related Items (14)

Critical surface of the hexagonal polygon model ⋮ Lattice gauge theory and a random-medium Ising model ⋮ Large \(N\) limit of the \(O(N)\) linear sigma model in 3D ⋮ Uniform Lipschitz functions on the triangular lattice have logarithmic variations ⋮ Macroscopic loops in the loop \(O(n)\) model at Nienhuis' critical point ⋮ Site monotonicity and uniform positivity for interacting random walks and the spin \(O(N)\) model with arbitrary \(N\) ⋮ Structure of Gibbs measure for planar FK-percolation and Potts models ⋮ Shifted critical threshold in the loop \(O(n)\) model at arbitrarily small \(n\) ⋮ Lectures on the Ising and Potts Models on the Hypercubic Lattice ⋮ Strongly correlated random interacting processes. Abstracts from the workshop held January 28 -- February 3, 2018 ⋮ Exponential decay in the loop \(O(n)\) model on the hexagonal lattice for \(n > 1\) and \(x<\frac{1}{\sqrt{3}}+\varepsilon (n)\) ⋮ Exponential decay of transverse correlations for \(O(N)\) spin systems and related models ⋮ Scaling limit of ballistic self-avoiding walk interacting with spatial random permutations ⋮ A variational principle for a non-integrable model

Cites Work

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