Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Renormalized energy between vortices in some Ginzburg-Landau models on
  2-dimensional Riemannian manifolds   We study a variational Ginzburg-Landau type model depending on a small
parameter $\varepsilon>0$ for (tangent) vector fields on a $2$-dimensional
Riemannian manifold $S$. As $\varepsilon\to 0$, these vector fields tend to
have unit length so they generate singular points, called vortices, of a
(non-zero) index if the genus $\mathfrak{g}$ of $S$ is different than $1$. Our
first main result concerns the characterization of canonical harmonic unit
vector fields with prescribed singular points and indices. The novelty of this
classification involves flux integrals constrained to a particular
vorticity-dependent lattice in the $2\mathfrak{g}$-dimensional space of
harmonic $1$-forms on $S$ if $\mathfrak{g}\geq 1$. Our second main result
determines the interaction energy (called renormalized energy) between vortex
points as a $\Gamma$-limit (at the second order) as $\varepsilon\to 0$. The
renormalized energy governing the optimal location of vortices depends on the
Gauss curvature of $S$ as well as on the quantized flux. The coupling between
flux quantization constraints and vorticity, and its impact on the renormalized
energy, are new phenomena in the theory of Ginzburg-Landau type models. We also
extend this study to two other (extrinsic) models for embedded hypersurfaces
$S\subset \mathbb{R}^3$, in particular, to a physical model for non-tangent
maps to $S$ coming from micromagnetics.

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The categories of this paper are: physics
24
The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
18
The categories of this paper are: econ
1
The categories of this paper are: cs
16
The categories of this paper are: stat
0
The categories of this paper are: hep-ph
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
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The categories of this paper are: alg-geom
14
The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc
32
The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th