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

Thermodynamic potential of a neutral two-dimensional (2D) Coulomb 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 even coupling constant.