Packing hard spheres with short-range attraction in infinite dimension: Phase structure and algorithmic implications
arXiv:1309.3218 · doi:10.1088/1742-6596/473/1/012020
Abstract
We study, via the replica method of disordered systems, the packing problem of hard-spheres with a square-well attractive potential when the space dimensionality, d, becomes infinitely large. The phase diagram of the system exhibits reentrancy of the liquid-glass transition line, two distinct glass states and a glass-to-glass transition, much similar to what has been previously obtained by Mode-Coupling Theory, numerical simulations and experiments. The presence of the phase reentrance implies that for a suitable choice of the intensity and attraction range, high-density sphere packings more compact than the one corresponding to pure hard-spheres can be constructed in polynomial time in the number of particles (at fixed, large d) for packing fractions smaller than 6.5 d 2^{-d}. Although our derivation is not a formal mathematical proof, we believe it meets the standards of rigor of theoretical physics, and at this level of rigor it provides a small improvement of the lower bound on the sphere packing problem.
18 pages, 7 figures -- Proceedings of the International Meeting on "Inference, Computation, and Spin Glasses", Sapporo, Japan, July 28-30, 2013
References in corpus (14)
- Packing Hyperspheres in High-Dimensional Euclidean Spaces
- Rigorous Inequalities between Length and Time Scales in Glassy Systems
- A Landscape Analysis of Constraint Satisfaction Problems
- Universal microstructure and mechanical stability of jammed packings
- Exact theory of dense amorphous hard spheres in high dimension. I. The free energy
- Robust Algorithm to Generate a Diverse Class of Dense Disordered and Ordered Sphere Packings via Linear Programming
- Dimensional Study of the Caging Order Parameter at the Glass Transition
- Glass transition of hard spheres in high dimensions
- Improved sphere packing lower bounds from Hurwitz lattices
- A Lattice Model for Colloidal Gels and Glasses
- Dynamic facilitation picture of a higher-order glass singularity
- Comment on ``Spherical 2 + p spin-glass model: An analytically solvable model with a glass-to-glass transition''
- Reply to Comment on ``Spherical 2+p spin-glass model: an analytically solvable model with a glass-to-glass transition''
- Dynamical arrest and replica symmetry breaking in attractive colloids