Ferroelectricity in Dipolar Liquids: The Role of Annealed Positional Disorder.

Ferroelectric ordering in polar liquids has been observed in numerical simulations and liquid-crystal experiments. Within the mean-field framework, this behavior remains associated with the sample-shape-dependent surface contribution to the free energy, which does not vanish in the thermodynamic limit due to the long-range nature of dipolar interactions. Yet, numerical simulations performed under conducting periodic boundary conditions, for which the surface contribution vanishes, still exhibit ferroelectric order, pointing to an intrinsic bulk origin of the transition. Moving beyond the mean-field approximation, Kirkwood's seminal study of the dielectric properties of polar liquids emphasized the role of hindered dipolar rotation in shaping the corresponding pair correlations. In Kirkwood's analysis, hindered rotation stems from the mean force between nearest-neighbor dipoles, placing the focus on local structure. Introducing a different perspective while retaining the central role of hindered rotation in the onset of ferroelectricity, the present study establishes, as an original finding, that annealed averaging of dipolar interactions over positional disorder generates hindered dipolar rotation that favors dipole alignment and can drive a bulk ferroelectric phase transition. As a result, unlike approaches centered on local structure, ferroelectricity emerges not in spite of the liquid nature, but because of it. Annealed averaging over positional disorder defines an effective dipolar interaction that is shorter-ranged than the bare potential. This is analogous to the Keesom interaction, where screening arises from annealed dipolar disorder. Derived within classical density functional theory, these findings are exact for dimensions