Complexity as the driving force for dynamical glassy transitions

TL;DR

This paper investigates the dynamical glass transition in a mean field spin glass model, highlighting how increasing complexity and metastable states drive the transition and influence thermodynamic properties.

Contribution

It introduces a detailed analysis of complexity and metastable states at the dynamical transition, revealing their role in glassy dynamics and thermodynamics.

Findings

Complexity increases as temperature decreases.

The total glassy free energy is below the paramagnetic one near Tc.

Multiple glassy states cause differences in specific heat and internal energy derivatives.

Abstract

Aspects of the dynamical glass transition are considered within a mean field spin glass model. At the dynamical transition the the system condenses in a state of lower entropy. The difference, the information entropy or complexity, is calculated by analysis of the metastable (TAP) states. It increases for lower temperatures, showing that more and more free energy barriers cannot be overcome on accessible times scales. Near $T_c$ the total glassy free energy lies below the paramagnetic one, which makes the transition unavoidable from a thermodynamic point of view. The multitude of glassy states implies an extensive difference between the average specific heat and the derivative of the average internal energy.