(a) Schematic mean field free energy profiles for supercooled liquids at the dynamical crossover temperature (dashed line), the Kauzmann temperature (solid line), and an intermediate temperature (dot-dashed line). In the mean field, the particle localization and the structural overlap are equivalent reaction coordinates. The secondary free energy minimum at demonstrates the existence of metastable structural states in supercooled liquids. (b) Free energy profiles calculated for the finite range Ising magnet analogous to the LJ liquid. The minimum size needed to escape the free energy minimum and thus reconfigure the liquid at is particles.
The distributions of interactions and local fields of the magnet analogous to the simulated LJ two compound glasses. In this mapping is directly related to the configurational entropy, . The fields are shown at , close to the dynamical crossover temperature.
Phase diagram of the Ising model with random bonds and fields adapted from Ref. 32. The parameters calculated for the magnet analogous to the LJ liquid (circular mark) indicate that the liquid would undergo a true phase transition at the ideal glass transition. The triangular and square marks indicate estimates of where the glass forming liquids, OTP and , would fall on the phase diagram.
(a) Relaxation times of the Ising model analogous to the LJ liquid (circles). The solid line gives relaxation times calculated from free energy barriers. The dashed lines show fits using relations derived in RFOT theory (see text). (b) The minimum region size able to irreversibly reconfigure.
Free energy profiles for different regions at . The distribution of free energy barriers gives rise to the stretched exponential relaxation behavior common to glassy systems.
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