Revisiting the replica theory of the liquid to ideal glass transition
Abstract
The replica theory of the "Random First Order Transition" (RFOT) from a supercooled liquid to an "ideal" glass of a system of "soft spheres" is revisited. Following the seminal work of Mézard and Parisi [J. Chem. Phys. 111, 1076 (1999)], the number m of weakly interacting replicas of the system is varied continuously from m = 2 to m < 1. Relevant order parameters and the free energy of the liquid and glass phases are calculated using the hypernetted chain (HNC) approximation for the pair correlation functions. The scenario observed for all m confirms the existence of two glass branches G_{1} and G_{2}. The latter has the lowest free energy for all m > 1, while the former has a lower free energy for m < 1 but is shown to be unstable against spinodal decomposition for any nonzero value of the attractive interreplica coupling. The critical temperature T_{cr} of the RFOT turns out to depend on m, which may be a byproduct of the approximation inherent in the HNC closure. The RFOT is predicted to be weakly first order, characterized by a small jump in density between the coexisting liquid and G_{2} phases for all m > 1. Estimating T_{cr} in the limit m → 1 requires a proper extrapolation of high resolution HNC calculations. The present protocol explores the behavior of the free energy of the ideal glass phase below T_{cr} as a function of m.
 Publication:

Journal of Chemical Physics
 Pub Date:
 April 2019
 DOI:
 10.1063/1.5088811
 Bibcode:
 2019JChPh.150o4504B