### 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 language | English (US) |
---|---|

Title of host publication | XVIIth International Congress on Mathematical Physics |

Subtitle of host publication | Aalborg, Denmark, 6-11 August 2012 |

Publisher | World Scientific Publishing Co. |

Pages | 584-599 |

Number of pages | 16 |

ISBN (Electronic) | 9789814449243 |

ISBN (Print) | 9789814449236 |

DOIs | |

State | Published - 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)

## Fingerprint Dive into the research topics of '2D coulomb gas, abrikosov lattice and renormalized energy'. Together they form a unique fingerprint.

## Cite this

*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