Order in glassy systems

TL;DR

This paper introduces a measurable correlation length in glassy systems based on density profiles, which diverges with the slow relaxation timescale, and discusses how complexity measures can reveal the underlying transition mechanisms.

Contribution

It proposes a method to measure a correlation length in glassy systems from density profiles and links it to the divergence of relaxation times, testing theoretical scenarios.

Findings

Correlation length diverges with slow timescale

Complexity measures distinguish transition mechanisms

Supports the 'Random First Order' scenario

Abstract

A directly measurable correlation length may be defined for systems having a two-step relaxation, based on the geometric properties of density profile that remains after averaging out the fast motion. We argue that the length diverges if and when the slow timescale diverges, whatever the microscopic mechanism at the origin of the slowing down. Measuring the length amounts to determining explicitly the complexity from the observed particle configurations. One may compute in the same way the Renyi complexities K_q, their relative behavior for different q characterizes the mechanism underlying the transition. In particular, the 'Random First Order' scenario predicts that in the glass phase K_q=0 for q>x, and K_q>0 for q<x, with x the Parisi parameter. The hypothesis of a nonequilibrium effective temperature may also be directly tested directly from configurations.