Ferroelectricity in dipolar liquids: from an exactly solvable model in the large-dimensional limit to finite dimensions

TL;DR

This work shows that ferroelectric order can emerge in dipolar liquids when the positional degrees of freedom are annealed and the dipolar interaction is regularized to be isotropic and short-ranged. In the $d\to\infty$ limit, a density-functional framework with a second-virial truncation yields an exact result where the excess free energy is minimized by full dipole alignment, despite screening of the long-range tail by orientational averaging. Finite-$d$ extensions use an optimized cluster (renormalized) approach, proving that the second-order virial contribution is still minimized by ferroelectric order for $d\ge3$, with the exponential approximation providing broad validity beyond low densities. Overall, the paper argues that annealed positional disorder is a universal, constitutive driver of ferroelectricity in dipolar liquids, yielding a universal, screened, ferroelectric-like interaction and suggesting avenues to study quenched disorder and dipolar glasses via replicated-liquid theory.

Abstract

A medium, liquid in its positional degrees of freedom, exhibits in real space a homogeneous single-particle density and an isotropic linear response to perturbations of the density field. Under the hypothesis that, if the anisotropic dipolar interaction is a weak perturbation of the isotropic reference system potential, this condition persists in a dipolar liquid for any dipole configuration, a regularization of the dipolar potential can be introduced. This developments lead to the definition of a screened dipolar interaction that is isotropic, short-ranged, and ferroelectric-like. In a classical density functional theory framework the model is exactly solvable in the limit of infinite dimensions, whereas approximations can be obtained in the case of finite dimensions $d \geq 3$ in the optimized cluster expansion scheme. In both cases, it is shown that the system can support a ferroelectric phase transition. The study relates the emergence of ferroelectricity in dipolar liquids to a constitutive property of the liquid state, i.e. annealed positional disorder.