Finite-Size Effects in Non-Neutral Two-Dimensional Coulomb Fluids

Abstract

Thermodynamic potential of a neutral two-dimensional (2D) Cou\-lomb fluid, confined to a large domain with a smooth boundary, exhibits at any (inverse) temperature $\beta$ a logarithmic finite-size correction term whose universal prefactor depends only on the Euler number of the domain and the conformal anomaly number $c=-1$. A minimal free boson conformal field theory, which is equivalent to the 2D symmetric two-component plasma of elementary $\pm e$ charges at coupling constant $\Gamma =\beta e^2$, was studied in the past. It was shown that creating a non-neutrality by spreading out a charge $Qe$ at infinity modifies the anomaly number to $c(Q,\Gamma )=-1+3\Gamma Q^2$. Here, we study the effect of non-neutrality on the finite-size expansion of the free energy for another Coulomb fluid, namely the 2D one-component plasma (jellium) composed of identical pointlike $e$-charges in a homogeneous background surface charge density. For the disk geometry of the confining domain we find that the non-neutrality induces the same change of the anomaly number in the finite-size expansion. We derive this result first at the free-fermion coupling $\Gamma \equiv \beta e^2=2$ and then, by using a mapping of the 2D one-component plasma onto an anticommuting field theory formulated on a chain, for an arbitrary coupling constant.

14 pages

References in corpus (6)

• Relations Among Two Methods for Computing the Partition Function of the Two-Dimensional One-Component Plasma
• Exact Energy Computation of the One Component Plasma on a Sphere for Even Values of the Coupling Parameter
• Counter-ions between or at asymmetrically charged walls: 2D free-fermion point
• Counter-Ions Near a Charged Wall: Exact Results for Disc and Planar Geometries
• Screening of an electrically charged particle in a two-dimensional two-component plasma at $\Gamma =2$
• Amplitude Function of Asymptotic Correlations Along Charged Wall in Coulomb Fluids

Cited by in corpus (2)

• Attraction of like-charged walls with counterions only: Exact results for the 2D cylinder geometry
• Logarithmic Finite-Size Correction in Non-neutral Two-Component Plasma on Sphere