A note on weakly discontinuous dynamical transitions
Silvio Franz, Giorgio Parisi, Federico Ricci-Tersenghi, Tommaso Rizzo,, Pierfrancesco Urbani
TL;DR
This paper investigates the behavior of Mode Coupling discontinuous transitions near the $A_3$ point, revealing universal features and proposing new perspectives for analyzing these transitions in complex systems.
Contribution
It provides a detailed analysis of the $A_3$ limit, highlighting universal properties and offering novel insights into Mode Coupling equations.
Findings
Structural relaxation and fluctuations exhibit universal form near the $A_3$ point.
Approaching the $A_3$ point simplifies the analysis of Mode Coupling transitions.
New methods for examining Mode Coupling equations are suggested.
Abstract
We analyze Mode Coupling discontinuous transition in the limit of vanishing discontinuity, approaching the so called "" point. In these conditions structural relaxation and fluctuations appear to have universal form independent from the details of the system. The analysis of this limiting case suggests new ways for looking at the Mode Coupling equations in the general case.
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