The High Temperature Crossover for General 2D Coulomb Gases

Akemann G, Byun S-S (2019)
JOURNAL OF STATISTICAL PHYSICS 175(6): 1043-1065.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Akemann, GernotUniBi; Byun, Sung-Soo
Abstract / Bemerkung
We consider N particles in the plane, influenced by a general external potential, that are subject to the Coulomb interaction in two dimensions at inverse temperature . At large temperature, when scaling =2c/N with some fixed constant c>0, in the large-N limit we observe a crossover from Ginibre's circular law or its generalisation to the density of non-interacting particles at =0. Using Ward identities and saddle point methods we derive a partial differential equation of generalised Liouville type for the crossover density. For radially symmetric potentials we present some asymptotic results and give examples for the numerical solution of the crossover density. These findings generalise previous results when the interacting particles are confined to the real line. In that situation we derive an integral equation for the resolvent valid for a general potential as well, and present the analytic solution for the density in the case of a Gaussian plus logarithmic potential.
Stichworte
2D Coulomb gases; Normal random matrices; High temperature crossover
Erscheinungsjahr
2019
Zeitschriftentitel
JOURNAL OF STATISTICAL PHYSICS
Band
175
Ausgabe
6
Seite(n)
1043-1065
ISSN
0022-4715
eISSN
1572-9613
Page URI
https://pub.uni-bielefeld.de/record/2936333

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Akemann G, Byun S-S. The High Temperature Crossover for General 2D Coulomb Gases. JOURNAL OF STATISTICAL PHYSICS. 2019;175(6):1043-1065.
Akemann, G., & Byun, S. - S. (2019). The High Temperature Crossover for General 2D Coulomb Gases. JOURNAL OF STATISTICAL PHYSICS, 175(6), 1043-1065. doi:10.1007/s10955-019-02276-6
Akemann, G., and Byun, S. - S. (2019). The High Temperature Crossover for General 2D Coulomb Gases. JOURNAL OF STATISTICAL PHYSICS 175, 1043-1065.
Akemann, G., & Byun, S.-S., 2019. The High Temperature Crossover for General 2D Coulomb Gases. JOURNAL OF STATISTICAL PHYSICS, 175(6), p 1043-1065.
G. Akemann and S.-S. Byun, “The High Temperature Crossover for General 2D Coulomb Gases”, JOURNAL OF STATISTICAL PHYSICS, vol. 175, 2019, pp. 1043-1065.
Akemann, G., Byun, S.-S.: The High Temperature Crossover for General 2D Coulomb Gases. JOURNAL OF STATISTICAL PHYSICS. 175, 1043-1065 (2019).
Akemann, Gernot, and Byun, Sung-Soo. “The High Temperature Crossover for General 2D Coulomb Gases”. JOURNAL OF STATISTICAL PHYSICS 175.6 (2019): 1043-1065.