### 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: 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 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Physics and Astronomy(all)

### 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

**2D coulomb gas, abrikosov lattice and renormalized energy.** / Serfaty, Sylvia.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

*XVIIth International Congress on Mathematical Physics: Aalborg, Denmark, 6-11 August 2012.*World Scientific Publishing Co., pp. 584-599. https://doi.org/10.1142/9789814449243_0061

}

TY - CHAP

T1 - 2D coulomb gas, abrikosov lattice and renormalized energy

AU - Serfaty, Sylvia

PY - 2013/1/1

Y1 - 2013/1/1

N2 - 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.

AB - 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.

KW - Abrikosov lattice

KW - Coulomb gas

KW - Ginibre ensemble

KW - Ginzburg-Landau

KW - Log gases

KW - Plasma

KW - Renormalized energy

KW - Superconductivity

KW - Vortices

UR - http://www.scopus.com/inward/record.url?scp=84974822472&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84974822472&partnerID=8YFLogxK

U2 - 10.1142/9789814449243_0061

DO - 10.1142/9789814449243_0061

M3 - Chapter

SN - 9789814449236

SP - 584

EP - 599

BT - XVIIth International Congress on Mathematical Physics: Aalborg, Denmark, 6-11 August 2012

PB - World Scientific Publishing Co.

ER -