Many materials can be modeled either as discrete systems or as continua, depending on the
scale. At intermediate scales it is necessary to understand the transition from discrete to …

We study a nearest neighbors ferromagnetic classical spin system on the square lattice in
which the spin field is constrained to take values in a discretization of the unit circle …

We consider a classical Heisenberg system of S 2 spins on a square lattice of spacing ɛ. We
introduce a magnetic anisotropy by constraining the out-of-plane component of each spin to …

We investigate the relationship between the N‐clock model (also known as planar Potts
model or‐model) and the XY model (at zero temperature) through a Γ‐convergence analysis …

We study the variational limit of the frustrated J 1–J 2–J 3 spin model on the square lattice in
the vicinity of the ferromagnet/helimagnet transition point as the lattice spacing vanishes. We …

A neural network is a powerful tool that can uncover hidden laws beyond human intuition.
However, it often appears as a black box due to its complicated nonlinear structures. By …

Coarse graining and large-N behavior of the d-dimensional N-clock model Page 1 Interfaces Free
Bound. 23 (2021), 323–351 © 2021 European Mathematical Society Published by EMS Press This …

We consider the numerical approximation of a continuum model of antiferromagnetic and
ferrimagnetic materials. The state of the material is described in terms of two unit-length …

In dieser Arbeit werden variationelle Modelle für Mikrostrukturen in speziellen Materialien
untersucht, um die Strukturformation zu verstehen und Eigenschaften von Grundzuständen …

On a two-dimensional Riemannian manifold without boundary we consider the variational
limit of a family of functionals given by the sum of two terms: a Ginzburg-Landau and a …