Exponential decay in the loop \(O(n)\) model on the hexagonal lattice for \(n > 1\) and \(x<\frac{1}{\sqrt{3}}+\varepsilon (n)\)

DOI10.1007/978-3-030-60754-8_21zbMath1469.60330arXiv1810.11302OpenAlexW3141162719MaRDI QIDQ1983062

Ioan Manolescu, Alexander Glazman

Publication date: 15 September 2021

Full work available at URL: https://arxiv.org/abs/1810.11302

zbMATH Keywords

lattice modelsIsing modelphase diagramstatistical mechanicsloop models\(O(n)\) modelenhancement percolation

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)

Related Items (3)

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 ⋮ Height function delocalisation on cubic planar graphs

Cites Work

• The connective constant of the honeycomb lattice equals \(\sqrt{2+\sqrt 2}\)
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• Conformal invariance in random cluster models. I: Holomorphic fermions in the Ising model
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• A guide to stochastic Löwner evolution and its applications
• Intersecting loop models on \({\mathbb Z}^ d\): rigorous results.
• Shifted critical threshold in the loop \(O(n)\) model at arbitrarily small \(n\)
• The scaling limit of critical Ising interfaces is \(\mathrm{CLE}_3\)
• Uniform Lipschitz functions on the triangular lattice have logarithmic variations
• Macroscopic loops in the loop \(O(n)\) model at Nienhuis' critical point
• Critical percolation in the plane: conformal invariance, Cardy's formula, scaling limits
• Lectures on the Spin and Loop O(n) Models
• Statistical Mechanics of Lattice Systems
• The Random-Cluster Model
• Crystal Statistics. I. A Two-Dimensional Model with an Order-Disorder Transition

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