Two-dimensional Coulomb Systems in a disk with Ideal Dielectric Boundaries

Abstract

We consider two-dimensional Coulomb systems confined in a disk with ideal dielectric boundaries. In particular we study the two-component plasma in detail. When the coulombic coupling constant $\Gamma =2$ the model is exactly solvable. We compute the grand-potential, densities and correlations. We show that the grand-potential has a universal logarithmic finite-size correction as predicted in previous works. This logarithmic finite-size correction is also checked in another solvable model: the one-component plasma.

29 pages, 8 figures

References in corpus (2)

• Coulomb Systems Seen as Critical Systems: Ideal Conductor Boundaries
• Surface Tension of a Metal-Electrolyte Boundary: Exactly Solvable Model

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