When is a conductor not perfect? Sum rules fail under critical fluctuations.

Perfect screening of all charges characterizes a conductor, a fact embodied in the Stillinger-Lovett sum rule: namely, the charge-charge correlation or structure factor, S(ZZ)(k), varies with momentum transfer k→0 as ξ(D)(2)k(2) where the Debye length ξ(D) is a universal function, √k(B)T/ρq(D)(2), of T and the ion density ρ, with a scaled charge q(D). For a charge-symmetric hard-sphere electrolyte our grand canonical simulations, with a new finite-size scaling device, confirm the Stillinger-Lovett rule except, contrary to current theory, for its failure at criticality. Furthermore, the k(4) term in the S(ZZ)(k) expansion is found to diverge like the compressibility when T→T(c) at ρ(c).