Quantitative approximation schemes for glasses

Abstract

By means of a systematic expansion around the infinite-dimensional solution, we obtain an approximation scheme to compute properties of glasses in low dimensions. The resulting equations take as input the thermodynamic and structural properties of the equilibrium liquid, and from this they allow one to compute properties of the glass. They are therefore similar in spirit to the Mode-Coupling approximation scheme. Our scheme becomes exact, by construction, in dimension $d\to \infty$ and it can be improved systematically by adding more terms in the expansion.

22 pages, 4 figures

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Cited by in corpus (19)

• Glass and Jamming Transitions: From Exact Results to Finite-Dimensional Descriptions
• A characteristic energy scale in glasses
• Mean field theory of the swap Monte Carlo algorithm
• A simple theory for the dynamics of mean-field-like models of glass-forming fluids
• Out-of-equilibrium dynamical equations of infinite-dimensional particle systems. I. The isotropic case
• Memory formation in jammed hard spheres
• Interplay between percolation and glassiness in the random Lorentz gas
• Mean-field caging in a random Lorentz gas
• The dimensional evolution of structure and dynamics in hard sphere liquids
• Thermodynamic stability of hard sphere crystals in dimensions 3 through 10
• A self-consistent field theory of density correlations in classical fluids
• Jamming, relaxation, and memory in a structureless glass former
• Effect of particle exchange on the glass transition of binary hard spheres
• Bridging the gap between correlation entropy functionals in the mean spherical and the hypernetted chain approximations: a field theoretic description
• Dynamics and fluctuations of minimally-structured glass formers
• Comment on "Explicit Analytical Solution for Random Close Packing in $d=2$ and $d=3$"
• Free-energy functional of instantaneous correlation field in liquids: field-theoretic derivation of the closures
• Replica Field Theory for a Generalized Franz--Parisi Potential of Inhomogeneous Glassy Systems: New Closure and the Associated Self-Consistent Equation
• Gradient descent dynamics and the jamming transition in infinite dimensions