Glass transitions and scaling laws within an alternative mode-coupling theory
arXiv:1504.01290 · doi:10.1103/PhysRevE.91.042117
Abstract
Idealized glass transitions are discussed within a novel mode-coupling theory (TMCT) proposed by Tokuyama(Physica A 395,31(2014)). This is done in order to identify common grounds with and differences to the conventional mode-coupling theory (MCT). It is proven that both theories imply the same scaling laws for the transition dynamics, which are characterized by two power-law decay functions and two diverging power-law time scales. However, the values for the corresponding anomalous exponents calculated within both theories differ from each other. It is proven that the TMCT, contrary to the MCT, does not describe transitions with continuously vanishing arrested parts of the correlation functions. It is also demonstrated for a schematic model that the TMCT neither leads to the MCT scenarios for transition-line crossings nor for the appearance of higher-order glass-transition singularities.
References in corpus (5)
- Cooperativity Beyond Caging: Generalized Mode Coupling Theory
- Glass transition of hard spheres in high dimensions
- Long-Wavelength Anomalies in the Asymptotic Behavior of Mode-Coupling Theory
- Recursion formulas for nonlinear density fluctuations near the glass transition
- Comment on "Mode-Coupling Theory as a Mean-Field Description of the Glass Transition"