2D coulomb gas, abrikosov lattice and renormalized energy

S. Serfaty

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

In joint work with Etienne Sandier, we studied the statistical mechanics of a classical twodimensional Coulomb gas, particular cases of which also correspond to random matrix ensembles. We connect the problem to the “renormalized energy” W, a Coulombian interaction for an infinite set of points in the plane that we introduced in connection to the Ginzburg-Landau model, and whose minimum is expected to be achieved by the “Abrikosov” triangular lattice. Results include a next order asymptotic expansion of the partition function, and various characterizations of the behavior of the system at the microscopic scale. When the temperature tends to zero we show that the system tends to “crystallize” to a minimizer of W.

Original languageEnglish (US)
Title of host publicationXVIIth International Congress on Mathematical Physics
Subtitle of host publicationAalborg, Denmark, 6-11 August 2012
PublisherWorld Scientific Publishing Co.
Pages584-599
Number of pages16
ISBN (Electronic)9789814449243
ISBN (Print)9789814449236
DOIs
StatePublished - Jan 1 2013

Keywords

  • Abrikosov lattice
  • Coulomb gas
  • Ginibre ensemble
  • Ginzburg-Landau
  • Log gases
  • Plasma
  • Renormalized energy
  • Superconductivity
  • Vortices

ASJC Scopus subject areas

  • Physics and Astronomy(all)

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    Serfaty, S. (2013). 2D coulomb gas, abrikosov lattice and renormalized energy. In XVIIth International Congress on Mathematical Physics: Aalborg, Denmark, 6-11 August 2012 (pp. 584-599). World Scientific Publishing Co.. https://doi.org/10.1142/9789814449243_0061