This paper aims at building a variational approach to the dynamics of discrete topological
singularities in two dimensions, based on Γ-convergence. We consider discrete systems …

We consider sequences of quadratic nonlocal functionals, depending on a small parameter,
that approximate the Dirichlet integral by a well-known result by Bourgain, Brezis, and …

We introduce and discuss discrete two-dimensional models for XY spin systems and screw
dislocations in crystals. We prove that, as the lattice spacing ε tends to zero, the relevant …

We study the magnetic energy of magnetic polymer composite materials as the average
distance between magnetic particles vanishes. We model the position of these particles in …

We formulate a variational model for a geometrically necessary screw dislocation in an anti-
plane lattice model at zero temperature. Invariance of the energy functional under lattice …

In this paper we rigorously investigate the emergence of defects on Nematic Shells with a
genus different from one. This phenomenon is related to a non-trivial interplay between the …

We describe the emergence of topological singularities in periodic media within the
Ginzburg–Landau model and the core-radius approach. The energy functionals of both …

We study the discrete-to-continuum variational limit of the J_1-J_3 spin model on the square
lattice in the vicinity of the ferromagnet/helimagnet transition point as the lattice spacing …

A key question in the analysis of discrete models for material defects, such as vortices in
spin systems and superconductors or isolated dislocations in metals, is whether information …

We study the discrete-to-continuum variational limit of the antiferromagnetic XY model on the
two-dimensional triangular lattice in the vortex regime. Within this regime, the spin system …