Fluctuations in Electrolytes: The Lebowitz and Other Correlation Lengths

Explicit low-density expansions (using Meeron and hypernetted-chain graphical resummations) are reported for various charge and density correlation lengths in hard-sphere electrolytes with general valences, z_σ, and diameters, a_στ. The “Lebowitz length” quantifies the area lawfor charge fluctuations, 〈Q_Λ²〉, in a large domain Λ; it approaches but differs from the Debye and other correlation lengths. All corresponding, universal limiting-law predictions of generalized Debye-Hückel (GDH) theory (Lee and Fisher, 1996–1997) prove exact, thus validating GDH theory as a basis for studying anomalies in Coulombic criticality.