Logarithmic critical slowing down in complex systems: from statics to dynamics
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909209706102784 |
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| author | Leuzzi, Luca Rizzo, Tommaso |
| author_facet | Leuzzi, Luca Rizzo, Tommaso |
| contents | 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 $λ=1$. We obtain a quantitative expression for the parameter $μ$ of the logarithmic decay in terms of cumulants of the overlap, which are physically observable in experiments or numerical simulations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_07565 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Logarithmic critical slowing down in complex systems: from statics to dynamics Leuzzi, Luca Rizzo, Tommaso Disordered Systems and Neural Networks Materials Science Soft Condensed Matter Statistical Mechanics 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 $λ=1$. We obtain a quantitative expression for the parameter $μ$ of the logarithmic decay in terms of cumulants of the overlap, which are physically observable in experiments or numerical simulations. |
| title | Logarithmic critical slowing down in complex systems: from statics to dynamics |
| topic | Disordered Systems and Neural Networks Materials Science Soft Condensed Matter Statistical Mechanics |
| url | https://arxiv.org/abs/2403.07565 |