Density Correlations in the Two-Dimensional Coulomb Gas
Abstract
We consider a two-dimensional Coulomb gas of positive and negative pointlike unit charges interacting via a logarithmic potential. The density (rather than the charge) correlation functions are studied. In the bulk, the form-factor theory of an equivalent sine-Gordon model is used to determine the density correlation length. At the surface of a rectilinear plain wall, the universality of the asymptotic behavior of the density correlations is suggested. A scaling analysis implies a local form of the compressibility sum rule near a hard wall. A symmetry of the Coulomb system with respect to the M\"obius conformal transformation, which induces a gravitational source acting on the particle density, is established. Among the consequences, a universal term of the finite-size expansion of the grand potential is derived exactly for a disk geometry of the confining domain.
Cite
@article{arxiv.cond-mat/0105604,
title = {Density Correlations in the Two-Dimensional Coulomb Gas},
author = {L. Šamaj and B. Jancovici},
journal= {arXiv preprint arXiv:cond-mat/0105604},
year = {2007}
}
Comments
35 pages, Latex