Evidence of a higher-order singularity in dense short-ranged attractive colloids

TL;DR

This paper identifies a higher-order glass transition singularity in dense colloids with short-range attraction, revealing unique dynamic behaviors like logarithmic decay and sublinear mean square displacement near the $A_4$ point.

Contribution

It combines theoretical and numerical methods to locate and characterize the $A_4$ singularity in a colloidal model with short-range attraction, advancing understanding of complex glass transitions.

Findings

Detection of logarithmic decay of density correlations near $A_4$

Observation of sublinear power-law increase in mean square displacement

The range of potential influences the time window of anomalous dynamics

Abstract

We study a model in which particles interact through a hard-core repulsion complemented by a short-ranged attractive potential, of the kind found in colloidal suspensions. Combining theoretical and numerical work we locate the line of higher-order glass transition singularities and its end-point -- named $A_4$ -- on the fluid-glass line. Close to the $A_4$ point, we detect logarithmic decay of density correlations and sub linear power-law increase of the mean square displacement, for time intervals up to four order of magnitudes. We establish the presence of the $A_4$ singularity by studying how the range of the potential affects the time-window where anomalous dynamics is observed.