Spin-glass charge ordering in ionic liquids

Ionic liquids form intricate nanostructures, both in the bulk and near charged surfaces. We show that given the ionic positions from molecular simulations, the ionic charges minimize a ``spin-glass'' Hamiltonian for nearest-neighbor interactions with remarkable accuracy, for both room-temperature ionic liquids and water-in-salt electrolytes. Thus, long-range charge oscillations in ionic liquids result from positional ordering, which is maximized in ionic solids but gradually disappears with added solvent, increased temperature, or by complex molecular structures. As the electrolyte becomes more disordered, geometrical frustration in the spin-glass ground state reduces correlation lengths. Eventually, thermal fluctuations excite the system from its ground state and Poisson-Boltzmann behavior is recovered. More generally, spin-glass ordering arises in any liquid with antiferromagnetic correlations, such as molten salt or the two-dimensional vortex patterns found in superfluids and bacterial turbulence.