Electric field fluctuations in the two-dimensional Coulomb fluid

TL;DR

This paper investigates electric field fluctuations in a two-dimensional Coulomb fluid, revealing phase transitions, ensemble differences, and mechanisms relevant to ionic liquids and spin ice, supported by simulations and theoretical comparisons.

Contribution

It provides the first detailed simulation and analysis of electric field structure factors across phase transitions in 2D Coulomb fluids, highlighting ensemble effects and experimental relevance.

Findings

Singular changes in structure factor at BKT transition

Ensemble inequivalence in poor electrolyte phase

Identification of 'underscreening' and 'pinch point' mechanisms

Abstract

The structure factor for electric field correlations in the two dimensional Coulomb fluid is simulated and compared to theories of the dielectric function. Singular changes in the structure factor occur at the BKT insulator to conductor transition, as well as at a higher temperature correlation transition between a poor electrolyte and perturbed Debye-H\"uckel fluid. Structure factors are found to differ in the canonical and grand canonical ensembles, with the poor electrolyte showing full ensemble inequivalence. We identify mechanisms of `underscreening' and `pinch point' scattering that are relevant to experiments on ionic liquids and artificial spin ice respectively.