Kinetically Constrained Models

TL;DR

This paper reviews recent advances in kinetically constrained models (KCMs) for glass formers, focusing on ergodicity breaking, relaxation dynamics, dynamical heterogeneities, and phase coexistence phenomena.

Contribution

It provides a comprehensive summary of KCMs, highlighting new insights into their dynamical behavior and phase transitions relevant to glassy systems.

Findings

Ergodicity breaking transitions can occur in KCMs.

Relaxation times depend on control parameters like density or temperature.

KCMs predict significant dynamical heterogeneities and phase coexistence phenomena.

Abstract

In this chapter we summarize recent developments in the study of kinetically constrained models (KCMs) as models for glass formers. After recalling the definition of the KCMs which we cover we study the possible occurrence of ergodicity breaking transitions and discuss in some detail how, before any such transition occurs, relaxation timescales depend on the relevant control parameter (density or temperature). Then we turn to the main issue: the prediction of KCMs for dynamical heterogeneities. We focus in particular on multipoint correlation functions and susceptibilities, and decoupling in the transport coefficients. Finally we discuss the recent view of KCMs as being at first order coexistence between an active and an inactive space-time phase.