Charge and density fluctuations in electrolytes: The Lebowitz and other correlation lengths

Puzzling features in the observed critical behavior of electrolyte solution s have stimulated the development of a generalized Debye-Huckel (GDH) theor y which yields approximate but thermodynamically consistent correlation fun ctions. Since understanding charge and density fluctuations proves crucial, we have employed Meeron's (1958) analysis supplemented by the HNC graphica l resummation (1959) for the unrestricted primitive model (with distinct di ameters, e.g., a(++), a(+-), and a(--)) to compute exact low-density expans ions, with leading correction terms, for the zeroth, second, and fourth mom ent charge-charge and density-density correlation lengths, xi(Z,1)(T, rho), xi(N,1)(T, rho), etc., and for the Lebowitz length, xi(L)(T, rho), The lat ter quantifies the area law of charge fluctuations, [Q(Lambda)(2)], in a la rge domain Lambda. All results confirm the predictions of the GDH approxima tion in leading orders which, thus, currently seems the best basis for stud ying criticality in ionic systems.