Charge and Density Fluctuations Lock Horns : Ionic Criticality with Power-Law Forces

Abstract

How do charge and density fluctuations compete in ionic fluids near gas-liquid criticality when quantum mechanical effects play a role ? To gain some insight, long-range $Φ^{\mathcal{L}}_{\pm \pm} / r^{d+σ}$ interactions (with $σ>0$), that encompass van der Waals forces (when $σ= d = 3$), have been incorporated in exactly soluble, $d$-dimensional 1:1 ionic spherical models with charges $\pm q_0$ and hard-core repulsions. In accord with previous work, when $d>\min \{σ, 2\}$ (and $q_0$ is not too large), the Coulomb interactions do not alter the ($q_0 = 0$) critical universality class that is characterized by density correlations at criticality decaying as $1/r^{d-2+η}$ with $η= \max \{0, 2-σ\}$. But screening is now algebraic, the charge-charge correlations decaying, in general, only as $1/r^{d+σ+4}$; thus $σ= 3$ faithfully mimics known \textit{non}critical $d=3$ quantal effects. But in the \textit{absence} of full ($+, -$) ion symmetry, density and charge fluctuations mix via a transparent mechanism: then the screening \textit{at criticality} is \textit{weaker} by a factor $r^{4-2η}$. Furthermore, the otherwise valid Stillinger-Lovett sum rule fails \textit{at} criticality whenever $η=0$ (as, e.g., when $σ>2$) although it remains valid if $η>0$ (as for $σ<2$ or in real $d \leq 3$ Ising-type systems).