Γ-convergence analysis for discrete topological singularities: The anisotropic triangular lattice and the long range interaction energy

DOI10.3233/ASY-151334zbMath1348.82018MaRDI QIDQ2805926

Lucia De Luca

Publication date: 13 May 2016

Published in: Asymptotic Analysis (Search for Journal in Brave)

zbMATH Keywords

dislocations\(\Gamma\)-convergenceXY spin systemsdiscrete topological singularities

Mathematics Subject Classification ID

Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Statistical thermodynamics (82B30)

Related Items (10)

Minimising movements for the motion of discrete screw dislocations along glide directions ⋮ \(\Gamma\)-convergence analysis of a generalized \(XY\) model: fractional vortices and string defects ⋮ Semidiscrete Modeling of Systems of Wedge Disclinations and Edge Dislocations via the Airy Stress Function Method ⋮ Screw dislocations in periodic media: variational coarse graining of the discrete elastic energy ⋮ Coarse-graining of a discrete model for edge dislocations in the regular triangular lattice ⋮ Motion of discrete interfaces on the triangular lattice ⋮ Defects in nematic shells: a \(\Gamma\)-convergence discrete-to-continuum approach ⋮ The antiferromagnetic \(XY\) model on the triangular lattice: chirality transitions at the surface scaling ⋮ Topological singularities in periodic media: Ginzburg-Landau and core-radius approaches ⋮ The antiferromagnetic xy model on the triangular lattice: topological singularities

Cites Work

• Existence and stability of a screw dislocation under anti-plane deformation
• Metastability and dynamics of discrete topological singularities in two dimensions: a \(\Gamma\)-convergence approach
• Variational analysis of the asymptotics of the \(XY\) model
• Lower bounds for the energy of unit vector fields and applications
• A product-estimate for Ginzburg-Landau and corollaries
• Degree theory of BMO. I: Compact manifolds without boundaries
• Discrete crystal elasticity and discrete dislocations in crystals
• Variational equivalence between Ginzburg-Landau, XY spin systems and screw dislocations energies
• Lower Bounds for Generalized Ginzburg--Landau Functionals
• Elastic Energy Stored in a Crystal Induced by Screw Dislocations: From Discrete to Continuous

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