Algebraic infection of charge correlations at the ionic critical point

We consider a classical two-component plasma analog of the restricted primitive model of electrolyte, where the hard-core interaction is replaced by a soft differentiable potential. Within the Born-Green-Yvon hierarchy for the equilibrium distribution functions, we shed light on an infection mechanism where the charge correlations are polluted by the density correlations at the critical point of the liquid-gas transition. This should imply an algebraic decay of critical charge correlations, consistently with the violation of the Stillinger-Lovett sum rule observed in Monte Carlo simulations. In connection with this effect of density correlations on the charge correlations, we also provide a discussion on an extended version of the Debye-Huckel theory that calculates charge correlations in the restricted primitive model for an externally imposed spatial fluctuation of charges.PACS Numbers: 05.30.-d, 05.70.Ce, 52.25.Kn.