Logarithmic critical slowing down in complex systems: from statics to dynamics

Author:

Luca Leuzzi, Tommaso Rizzo

Keyword:

Condensed Matter, Disordered Systems and Neural Networks, Disordered Systems and Neural Networks (cond-mat.dis-nn), Materials Science (cond-mat.mtrl-sci), Soft Condensed Matter (cond-mat.soft), Statistical Mechanics (cond-mat.stat-mech)

journal:

date:

2024-03-12 00:00:00

Abstract

We consider second-order phase transitions in which the order parameter is a replicated overlap matrix. We focus on a tricritical point that occurs in a variety of mean-field models and that, more generically, describes higher order liquid-liquid or liquid-glass transitions. We show that the static replicated theory implies slowing down with a logarithmic decay in time. The dynamical equations turn out to be those predicted by schematic Mode Coupling Theory for supercooled viscous liquids at a $A_3$ singularity, where the parameter exponent is $\lambda=1$. We obtain a quantitative expression for the parameter $\mu$ of the logarithmic decay in terms of cumulants of the overlap, which are physically observable in experiments or numerical simulations.

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