Critical Dynamics in Glassy Systems

Abstract

Critical dynamics in various glass models including those described by mode coupling theory is described by scale-invariant dynamical equations with a single non-universal quantity, i.e. the so-called parameter exponent that determines all the dynamical critical exponents. We show that these equations follow from the structure of the static replicated Gibbs free energy near the critical point. In particular the exponent parameter is given by the ratio between two cubic proper vertexes that can be expressed as six-point cumulants measured in a purely static framework.

24 pages, accepted for publication on PRE. Discussion of the connection with MCT added in the Conclusions

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Cited by in corpus (34)

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• Solution of the dynamics of liquids in the large-dimensional limit
• Growing timescales and lengthscales characterizing vibrations of amorphous solids
• Multiple reentrant glass transitions in confined hard-sphere glasses
• The many-body localized phase of the quantum random energy model
• Numerical detection of the Gardner transition in a mean-field glass former
• Following the evolution of glassy states under external perturbations: the full replica symmetry breaking solution
• Replica-symmetry-breaking transitions and off-equilibrium dynamics
• Marginally stable phases in mean-field structural glasses
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• Out-of-equilibrium dynamical equations of infinite-dimensional particle systems. I. The isotropic case
• Static replica approach to critical correlations in glassy systems
• Long-wavelength fluctuations lead to a model of the glass crossover
• Diluted Mean-Field Spin-Glass Models at Criticality
• Dynamical Landau Theory of the Glass Crossover
• Solvable Models of Supercooled Liquids in Three Dimensions
• Dynamical Mean-Field Theory and Aging Dynamics
• Brownian dynamics: from glassy to trivial
• Super-Cooled Liquids: Equivalence between Mode-Coupling Theory and Replica Approach
• Critical Off-Equilibrium Dynamics in Glassy Systems
• Numerical test of the replica-symmetric Hamiltonian for the correlations of the critical state of spin glasses in a field
• Theory of heterogeneous viscoelasticity
• A note on weakly discontinuous dynamical transitions
• The Glass Crossover from Mean-Field Spin-Glasses to Supercooled Liquids
• Evidence of a second-order phase transition in the six-dimensional Ising spin glass in a field
• The Ising spin glass on random graphs at zero temperature: not all spins are glassy in the glassy phase
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• Replica symmetry breaking in spin glasses in the replica-free Keldysh formalism
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• Logarithmic critical slowing down in complex systems: from statics to dynamics
• Following the evolution of metastable glassy states under external perturbations: compression and shear-strain
• Evidence of de Almeida-Thouless line below six dimensions