Algebraic infection of charge correlations of a classical electrolyte at the critical point of the liquid-gas transition

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 implies an algebraic decay of critical charge correlations. Such breakdown of exponential clustering should provide dielectric rather than conducting properties at the critical point, leading to the violation of certain charge-charge sum rules. This is in agreement with Monte Carlo simulations.