Super-Cooled Liquids: Equivalence between Mode-Coupling Theory and Replica Approach

Abstract

We show that the replica approach to glassy dynamics provides, in spite of its static nature, a characterization of critical dynamics in the $\beta$-regime of super-cooled liquids that is equivalent to the one of Mode-Coupling-Theory, both qualitatively and quantitatively. The nature and extent of this equivalence is discussed in connection to the main open problems of the current theory.

extended version, accepted for publication on PRE

References in corpus (18)

• On the Adam-Gibbs-Wolynes scenario for the viscosity increase in glasses
• Thermodynamics of glasses: a first principle computation
• Inhomogeneous Mode-Coupling Theory and Growing Dynamic Length in Supercooled Liquids
• Spontaneous and induced dynamic fluctuations in glass-formers I: General results and dependence on ensemble and dynamics
• A first principle computation of the thermodynamics of glasses
• Spontaneous and induced dynamic correlations in glass-formers II: Model calculations and comparison to numerical simulations
• A quantitative test of the mode-coupling theory of the ideal glass transition for a binary Lennard-Jones system
• The Debye-Waller factor of liquid silica: Theory and simulation
• Structural relaxation of polydisperse hard spheres: comparison of the mode-coupling theory to a Langevin dynamics simulation
• Field Theory of Fluctuations in Glasses
• Finite size effects in the dynamics of glass-forming liquids
• Quantitative field theory of the glass transition
• On the critical slowing down exponents of mode coupling theory
• Critical Dynamics in Glassy Systems
• Dynamic glass transition: bridging the gap between mode-coupling theory and the replica approach
• On the two-steps relaxation of mean-field glasses: p-spin model
• Dynamical critical exponents for the mean-field Potts glass
• Critical slowing down exponents in quenched disordered spin models for structural glasses: Random Orthogonal and related models

Cited by in corpus (8)

• Qualitative Features at the Glass Crossover
• Long-wavelength fluctuations lead to a model of the glass crossover
• Dynamical Landau Theory of the Glass Crossover
• Non-monotonic dynamic correlations beneath the surface of glass-forming liquids
• Quasi-equilibrium in glassy dynamics: a liquid theory approach
• The Glass Crossover from Mean-Field Spin-Glasses to Supercooled Liquids
• Theory of the $\beta$-Relaxation Beyond Mode-Coupling Theory: A Microscopic Treatment
• Full replica symmetry breaking in p-spin-glass-like systems