Mean-field theory of the glass transition in the one-component classical plasma

We study the supercooled-fluid region and the transition to an amorphous glassy state in the one-component classical plasma, within the replica-symmetry-breaking scenario developed by Franz and Parisi. This approach implements the slowing down of jumps of the disordered system between the minima in a rugged free-energy landscape by examining its correlations with a quenched replica as a function of their coupling expressed through a suitable short-range attractive potential. We carry out these calculations within a mean-field theory for the structure of a quenched-annealed mixture, using both the hypernetted chain approximation and a refinement to include an account of the bridge function. In both formulations our theoretical results demonstrate the existence of a glassy state for the plasma and yield an estimate of the phase-transition line, which has the form T∝ Z 2 n 1/3 where n is the particle number density, T the temperature and Z the valence, with a numerical coefficient which is about one eighth of that for equilibrium freezing. The consequences for various types of ionic fluids (simple molten salts, colloidal dispersions, and astrophysical plasmas) are illustrated.