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Logarithmic critical slowing down in complex systems: from statics to dynamics
- Source :
- Phys. Rev. B 109, 174211(2024)
- Publication Year :
- 2024
-
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.<br />Comment: 22 pages, 2 figures
Details
- Database :
- arXiv
- Journal :
- Phys. Rev. B 109, 174211(2024)
- Publication Type :
- Report
- Accession number :
- edsarx.2403.07565
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1103/PhysRevB.109.174211