Debye-Huckel theory for two-dimensional Coulomb systems living on a finite surface without boundaries
| dc.creator | Tellez, Gabriel | |
| dc.date | 2004-09-04 | |
| dc.date.accessioned | 2026-07-07T03:00:17Z | |
| dc.date.available | 2026-07-07T03:00:17Z | |
| dc.description | We study the statistical mechanics of a multicomponent two-dimensional Coulomb gas which lives on a finite surface without boundaries. We formulate the Debye--Huckel theory for such systems, which describes the low-coupling regime. There are several problems, which we address, to properly formulate the Debye--Huckel theory. These problems are related to the fact that the electric potential of a single charge cannot be defined on a finite surface without boundaries. One can only define properly the Coulomb potential created by a globally neutral system of charges. As an application of our formulation, we study, in the Debye--Huckel regime, the thermodynamics of a Coulomb gas living on a sphere of radius $R$. We find, in this example, that the grand potential (times the inverse temperature) has a universal finite-size correction $(1/3) \ln R$. We show that this result is more general: for any arbitrary finite geometry without boundaries, the grand potential has a finite-size correction $(χ/6) \ln R$, with $χ$ the Euler characteristic of the surface and $R^2$ its area. | |
| dc.identifier | https://arxiv.org/abs/cond-mat/0409093 | |
| dc.identifier | http://arxiv.org/abs/cond-mat/0409093 | |
| dc.identifier | Physica A 349, 155 (2005) | |
| dc.identifier | doi:10.1016/j.physa.2004.10.014 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/24784 | |
| dc.subject | Statistical Mechanics | |
| dc.title | Debye-Huckel theory for two-dimensional Coulomb systems living on a finite surface without boundaries | |
| dc.type | text |