The ideal glass transition of Hard Spheres
arXiv:cond-mat/0506445 · doi:10.1063/1.2041507
Abstract
We use the replica method to study the ideal glass transition of a liquid of identical Hard Spheres. We obtain estimates of the configurational entropy in the liquid phase, of the Kauzmann packing fraction, in the range 0.58--0.62, and of the random close packing density, in the range 0.64--0.67, depending on the approximation we use for the equation of state of the liquid. We also compute the pair correlation function in the glassy states (i.e., dense amorphous packings) and we find that the mean coordination number at random close packing is equal to 6. All these results compare well with numerical simulations and with other existing theories.
13 pages, 8 figures
References in corpus (3)
Cited by in corpus (58)
- Theoretical perspective on the glass transition and amorphous materials
- Jammed Hard-Particle Packings: From Kepler to Bernal and Beyond
- Mean field theory of hard sphere glasses and jamming
- Probing the equilibrium dynamics of colloidal hard spheres above the mode-coupling glass transition
- The glass transition of dense fluids of hard and compressible spheres
- Why is Random Close Packing Reproducible?
- Jamming versus Glass Transitions
- A Landscape Analysis of Constraint Satisfaction Problems
- Stability at Random Close Packing
- Fundamental challenges in packing problems: from spherical to non-spherical particles
- Basic Understanding of Condensed Phases of Matter via Packing Models
- A theory of amorphous packings of binary mixtures of hard spheres
- Compressing nearly hard sphere fluids increases glass fragility
- Do Binary Hard Disks Exhibit an Ideal Glass Transition?
- Mode-Coupling Theory as a Mean-Field Description of the Glass Transition
- Configurational entropy of hard spheres
- Perspective: Gardner Physics in Amorphous Solids and Beyond
- Entropy of jammed matter
- Constraints and vibrations in static packings of ellipsoidal particles
- Amorphous packings of hard spheres in large space dimension
- Dynamic light scattering measurements in the activated regime of dense colloidal hard spheres
- Mean field theory of the swap Monte Carlo algorithm
- Theory of the superglass phase
- Jamming in two-dimensional packings
- Equilibration of Concentrated Hard Sphere Fluids
- Estimating random close packing in polydisperse and bidisperse hard spheres via an equilibrium model of crowding
- Quantitative approximation schemes for glasses
- A Lattice Model for Colloidal Gels and Glasses
- The Inherent Structure Landscape Connection Between Liquids, Granular materials and the Jamming Phase Diagram
- Dynamic glass transition: bridging the gap between mode-coupling theory and the replica approach
- Sub-Jamming Transition in Binary Sphere Mixtures
- On the most compact regular lattice in large dimensions: A statistical mechanical approach
- Packing and Self-assembly of Truncated Triangular Bipyramids
- Long time limit of equilibrium glassy dynamics and replica calculation
- Free volume distribution of nearly jammed hard sphere packings
- Some recent theoretical results on amorphous packings of hard spheres
- Jamming III: Characterizing Randomness via the Entropy of Jammed Matter
- Critical scaling of jammed system after quench of temperature
- Another resolution of the configurational entropy paradox as applied to hard spheres
- Systematic expansion in the order parameter for replica theory of the dynamical glass transition
- Self-induced glassiness and pattern formation in spin systems subject to long-range interactions
- Aging and relaxation near Random Pinning Glass Transitions
- Model Energy Landscapes of Low-Temperature Fluids: Dipolar Hard Spheres
- On the high density behavior of Hamming codes with fixed minimum distance
- Glassy dynamics and hysteresis in a linear system of orientable hard rods
- Effect of particle exchange on the glass transition of binary hard spheres
- Dynamical arrest and replica symmetry breaking in attractive colloids
- Estimation of critical exponents from the cluster coefficients: Application to hard spheres
- Theory of simple glasses
- Hidden symmetries in jammed systems
- Comment to "Packing Hyperspheres in High-Dimensional Euclidean Space"
- Emergent universal long-range structure in random-organizing systems
- A note on Lee-Yang zeros in the negative half-plane
- Cavity approach to sphere packing in Hamming space
- Glass transition and random packing in the hard sphere system
- Absence of a structural glass phase in a monoatomic model liquid predicted to undergo an ideal glass transition
- Geometric and Topological Entropies of Sphere Packing
- An alternative, dynamic density functional-like theory for time-dependent density fluctuations in glass-forming fluids