Ergodicity and Slowing Down in Glass-Forming Systems with Soft Potentials: No Finite-Temperature Singularities

TL;DR

This paper demonstrates that glass-forming systems with soft potentials remain ergodic at all temperatures, lack finite-temperature singularities, and exhibit a super-Arrhenius relaxation without Kauzmann or Vogel-Fulcher crises.

Contribution

It provides a comprehensive analysis showing ergodicity, configurational entropy, and connectivity properties in soft-potential glass formers, challenging traditional views on glass transition singularities.

Findings

System remains ergodic at all temperatures

Configurational complexity is temperature independent

No Kauzmann or Vogel-Fulcher crises occur at finite temperatures

Abstract

The aim of this paper is to discuss some basic notions regarding generic glass forming systems composed of particles interacting via soft potentials. Excluding explicitly hard-core interaction we discuss the so called `glass transition' in which super-cooled amorphous state is formed, accompanied with a spectacular slowing down of relaxation to equilibrium, when the temperature is changed over a relatively small interval. Using the classical example of a 50-50 binary liquid of N particles with different interaction length-scales we show that (i) the system remains ergodic at all temperatures. (ii) the number of topologically distinct configurations can be computed, is temperature independent, and is exponential in N. (iii) Any two configurations in phase space can be connected using elementary moves whose number is polynomially bounded in N, showing that the graph of configurations has the `small world' property. (iv) The entropy of the system can be estimated at any temperature (or energy), and there is no Kauzmann crisis at any positive temperature. (v) The mechanism for the super-Arrhenius temperature dependence of the relaxation time is explained, connecting it to an entropic squeeze at the glass transition. (vi) There is no Vogel-Fulcher crisis at any finite temperature T>0