Coexistence of low and high overlap phases in a supercooled liquid: An integral equation investigation
Résumé
The pair structure, free energy and configurational overlap order parameter Q of an
annealed system of two weakly coupled replicas of a supercooled ”soft sphere” fluid
are determined by solving the hypernetted-chain (HNC) and self-consistent Rogers-
Young (RY) integral equations over a wide range of thermodynamic conditions ρ
(number-density), T (temperature) and inter-replicas couplings ε12. Analysis of the
resulting effective (or Landau) potential W(ρ,T;Q) and of its derivative w.r.t. Q
confirms the existence of a ”precursor transition” between weak and strong overlap
phases below a critical temperature Tc well above the temperature To of the ”ideal
glass” transition observed in the limit ε12 → 0. The precursor transition is signalled
by a loss of convexity of the potential W(Q) and by a concomitant discontinuity of
the order parameter Q just below Tc, which crosses over to a mean-field-like van
der Waals loop at lower temperatures. The HNC and RY equations lead to the same
phase transition scenario, with quantitative differences in the predicted temperatures
Tc and To.