Complexity as the driving force for glassy transitions

TL;DR

This paper investigates glassy transitions using toy models, revealing how complexity influences the dynamical and thermodynamic properties of systems like spin glasses and directed polymers.

Contribution

It introduces a detailed analysis of complexity's role in glassy transitions within mean field spin glass and directed polymer models, highlighting new insights into metastable states and phase behavior.

Findings

Dynamical transition involves entropy condensation in spin glasses.

Complexity analysis yields a well-behaved thermodynamics of the transition.

Polymer condensation occurs in highly degenerate metastable states at low temperature.

Abstract

The glass transition is considered within two toys models, a mean field spin glass and a directed polymer in a correlated random potential. In the spin glass model there occurs a dynamical transition, where the system condenses in a state of lower entropy. The extensive entropy loss, called complexity or information entropy, is calculated by analysis of the metastable (TAP) states. This yields a well behaved thermodynamics of the dynamical transition. The multitude of glassy states also implies an extensive difference between the internal energy fluctuations and the specific heat. In the directed polymer problem there occurs a thermodynamic phase transition in non-extensive terms of the free energy. At low temperature the polymer condenses in a set of highly degenerate metastable states.