Glass transitions and scaling laws within an alternative mode-coupling theory

TL;DR

This paper compares a new mode-coupling theory (TMCT) with the conventional MCT, showing they share scaling laws but differ in specific predictions about glass transition behaviors.

Contribution

It introduces and analyzes a novel TMCT, highlighting its similarities and differences with MCT, especially regarding transition dynamics and singularities.

Findings

Both theories predict the same scaling laws for transition dynamics.

TMCT does not describe transitions with vanishing arrested parts.

TMCT does not reproduce MCT scenarios for certain transition features.

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.