An investigation of the liquid to glass transition using integral equations for the pair structure of coupled...

Extensive numerical solutions of the hypernetted-chain (HNC) and Rogers-Young (RY) integral equations are presented for the pair structure of a system of two coupled replicae (1 and 2) of a "soft-sphere" fluid of atoms interacting via an inverse-12 pair potential. In the limit of vanishing inter-replica coupling ɛ12, both integral equations predict the existence of three branches of solutions: (1) A high temperature liquid branch (L), which extends to a supercooled regime upon cooling when the two replicae are kept at ɛ12 = 0 throughout; upon separating the configurational and vibrational contributions to the free energy and entropy of the L branch, the Kauzmann temperature is located where the configurational entropy vanishes. (2) Starting with an initial finite coupling ɛ12, two "glass" branches G1 and G2 are found below some critical temperature, which are characterized by a strong remnant spatial inter-replica correlation upon taking the limit ɛ12 → 0. Branch G2 is characterized by an increasing overlap order parameter upon cooling, and may hence be identified with the hypothetical "ideal glass" phase. Branch G1 exhibits the opposite trend of increasing order parameter upon heating; its free energy lies consistently below that of the L branch and above that of the G2 branch. The free energies of the L and G2 branches are found to intersect at an alleged "random first-order transition" (RFOT) characterized by weak discontinuities of the volume and entropy. The Kauzmann and RFOT temperatures predicted by RY differ significantly from their HNC counterparts.