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 + 3Gamma 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.