Coarse graining and large-\(N\) behavior of the \(d\)-dimensional \(N\)-clock model

DOI10.4171/IFB/456zbMath1476.49019arXiv2004.02217MaRDI QIDQ2244862

Matthias Ruf, Marco Cicalese, Gianluca Orlando

Publication date: 12 November 2021

Published in: Interfaces and Free Boundaries (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2004.02217

zbMATH Keywords

\(\varGamma\)-convergence\(XY\) model\(N\)-clock modelvector fields of bounded variation with values in the unit circle

Mathematics Subject Classification ID

Methods involving semicontinuity and convergence; relaxation (49J45) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Absolutely continuous real functions of several variables, functions of bounded variation (26B30)

Related Items (5)

Variational analysis of the \(J_1-J_2-J_3\) model: a non-linear lattice version of the Aviles-Giga functional ⋮ The \(N\)-clock model: variational analysis for fast and slow divergence rates of \(N\) ⋮ A classical \(\mathbb{S}^2\) spin system with discrete out-of-plane anisotropy: variational analysis at surface and vortex scalings ⋮ The antiferromagnetic \(XY\) model on the triangular lattice: chirality transitions at the surface scaling ⋮ The antiferromagnetic xy model on the triangular lattice: topological singularities

Cites Work

• Unnamed Item
• Unnamed Item
• Phase transitions in presence of surfactants: From discrete to continuum
• Domain formation in magnetic polymer composites: an approach via stochastic homogenization
• Interfaces, modulated phases and textures in lattice systems
• Defects in nematic shells: a \(\Gamma\)-convergence discrete-to-continuum approach
• Metastability and dynamics of discrete topological singularities in two dimensions: a \(\Gamma\)-convergence approach
• Variational analysis of the asymptotics of the \(XY\) model
• Phase and anti-phase boundaries in binary discrete systems: a variational viewpoint
• The approximation problem for Sobolev maps between two manifolds
• Design of lattice surface energies
• Continuum limit and stochastic homogenization of discrete ferromagnetic thin films
• Interfaces of ground states in Ising models with periodic coefficients
• On the continuity of functionals defined on partitions
• Variational problems with percolation: dilute spin systems at zero temperature
• The antiferromagnetic \(XY\) model on the triangular lattice: chirality transitions at the surface scaling
• Ginzburg-Landau functionals and renormalized energy: a revised \({\gamma}\)-convergence approach
• Frustrated ferromagnetic spin chains: a variational approach to chirality transitions
• \(\Gamma\)-convergence analysis of a generalized \(XY\) model: fractional vortices and string defects
• Variational equivalence between Ginzburg-Landau, XY spin systems and screw dislocations energies
• Discrete approximations to vector spin models
• Continuous spin mean-field models: Limiting kernels and Gibbs properties of local transforms
• Elements of Lipschitz topology
• Smoothed projections over weakly Lipschitz domains
• Variational Analysis of a Two-Dimensional Frustrated Spin System: Emergence and Rigidity of Chirality Transitions
• Elastic Energy Stored in a Crystal Induced by Screw Dislocations: From Discrete to Continuous
• $Q$-Tensor Continuum Energies as Limits of Head-to-Tail Symmetric Spin Systems
• Variational convergence for functionals of Ginzburg-Landau type
• Ginzburg-Landau vortices

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