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Topological Singularities in Periodic Media: Ginzburg–Landau and Core-Radius Approaches
(Journal article; Tidsskriftartikkel; Peer reviewed, 2021-12-20)
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 models are denoted by Eε,δ, where ε represent the coherence length (in the
Ginzburg–Landau model) or the core-radius size (in the core-radius approach) and
δ denotes the periodicity scale. We carry out the -convergence analysis ...
Asymptotic Behaviour of Ground States for Mixtures of Ferromagnetic and Antiferromagnetic Interactions in a Dilute Regime
(Journal article; Peer reviewed, 2018-04-30)
We consider randomly distributed mixtures of bonds of ferromagnetic and antiferromagnetic type in a two-dimensional square lattice with probability
1−p
1−p
and p, respectively, according to an i.i.d. random variable. We study minimizers of the corresponding nearest-neighbour spin energy on large domains in
Z
2
Z2
. We prove that there exists
p
0
p0
such that for
p≤
p
0
p≤p0
such ...