Density Correlations in the Two-Dimensional Coulomb Gas

Details Density Correlations in the Two-Dimensional Coulomb Gas Density Correlations in the Two-Dimensional Coulomb Gas

2001-05-31

arxiv.org/abs/cond-mat/0105604v1

J. Stat. Phys. 106 (2002) 323-355

Physics

Condensed Matter

Statistical Mechanics

35 pages, Latex

Scientific paper

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.

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