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Ge, Yuxin; Sandier, Etienne

Lattices with finite renormalized Coulombian interaction energy in the plane. (English) Zbl 1453.82007

Tunis. J. Math. 3, No. 1, 93-120 (2021).
Summary: We present criteria for a certain Coulombian interaction energy of infinitely many points in \(\mathbb{R}^d\), \(d\ge1\), with a uniformly charged background, to be finite, as well as examples. We also show that in this unbounded setting, it is not always possible to project an \(L^2_{\mathrm{loc}}\) vector field onto the set of gradients in a way that reduces its average \(L^2\) norm on large balls.

Cited in 3 Documents

MSC:

82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics
82B21 Continuum models (systems of particles, etc.) arising in equilibrium statistical mechanics

Keywords:

Coulombian renormalized energy; Fekete points; jellium; quasiperiodic lattices
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Full Text: DOI

References:

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