Mean-field theory of glass transitions

The experimental and the simulation results for the mean-square displacements in various systems are analyzed near glass transitions by employing the mean-field theory recently proposed. By comparing different glass transitions with each other from a unified point view, it is then shown that the mean-square displacements obey a logarithmic growth followed by a power-law growth of a super-diffusion type in β-relaxation stage. It is also shown that although the long-time self-diffusion coefficients are approximately described by a singular function of a control parameter with the same critical exponent for different systems where the singular point depends on the system, no divergence of any characteristic times, such as a β-relaxation time, is found near the singular point nor the glass transition point. A crossover point over which the supercooled liquid phase appears is also predicted theoretically. It is thus suggested that the present theory provides an useful tool to understand phenomena near the glass transition within the framework of the mean-square displacements.