Mean-field theory of hard sphere glasses and jamming

By Giorgio Parisi, Francesco Zamponi. 2008

551 citations recorded by the source corpus.

Hard spheres are ubiquitous in condensed matter: they have been used as models for liquids, crystals, colloidal systems, granular systems, and powders. Packings of hard spheres are of even wider interest, as they are related to important problems in information theory, such as digitalization of signals, error correcting codes, and optimization problems. In three dimensions the densest packing of identical hard spheres has been proven to be the FCC lattice, and it is conjectured that the closest packing is ordered (a regular lattice, e.g, a crystal) in low enough dimension. Still, amorphous packings have attracted a lot of interest, because for polydisperse colloids and granular materials the crystalline state is not obtained in experiments for kinetic reasons. We review here a theory of amorphous packings, and more generally glassy states, of hard spheres that is based on the replica method: this theory gives predictions on the structure and thermodynamics of these states. In dimensions between two and six these predictions can be successfully compared with numerical simulations. We will also discuss the limit of large dimension where an exact solution is possible. Some of the results we present here have been already published, but others are original: in particular we improved the discussion of the large dimension limit and we obtained new results on the correlation function and the contact force distribution in three dimensions. We also try here to clarify the main assumptions that are beyond our theory and in particular the relation between our static computation and the dynamical procedures used to construct amorphous packings.

Subfields: Biomedical Engineering, Condensed Matter Physics, Materials Chemistry

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Citations in the corpus

Universality of the SAT-UNSAT (jamming) threshold in non-convex continuous constraint satisfaction problems (2017, background): “Yet, one can restrict to the study of disordered configurations and in that case the SAT-UNSAT transition (also called “jamming transition” or “random close packing” in this case) has robustly universal critical properties [6,27].”
Mean-field avalanches in jammed spheres. (2016, background): “Our motivation to re-examine this problem in a general framework comes from the physics of soft spheres, in particular the jamming transition [13, 14, 15, 16, 17], where upon compression from a dilute phase, the system acquires mechanical stability.”
Aspects of non-equilibrium in classical and quantum systems: Slow relaxation and glasses, dynamical large deviations, quantum non-ergodicity, and open quantum dynamics (2017, background): “Due to (effective) frustration this free-energy landscape in configuration space is “rugged” with a potential proliferation of low lying states that under the right conditions may dominate the thermodynamics, leading eventually to a static singularity at some non-zero temperature [6, 23, 24].”
Edwards Statistical Mechanics for Jammed Granular Matter (2016, methodology): “Even if this condition did not appear in the original formulation by Edwards, it is nevertheless a quite obvious requirement, especially in light of analogous exact results in spin-glasses and hard-sphere glasses (Newman and Stein, 1999; Parisi and Zamponi, 2010).”
Collective cell guidance by cooperative intercellular forces (2010, unknown): “Cooperative motions emerge naturally in inert particulate systems that exhibit close-packing, structural disorder, and glassy dynamics, such as colloidal glasse”
The role of local structure in dynamical arrest (2014, background): “More specific reviews focus on certain theoretical aspects such as the energy landscape [191, 211, 454], dynamic heterogeniety [39, 146], Mode-Coupling Theory [85, 190], random first-order theory [317], replica theory [392], dynamic facilitation [81] and soft glassy rheology [477] and the insights g”
Fractal free energy landscapes in structural glasses (2014, background): “Slow compaction of the fluid makes it fall out of equilibrium near the dynamical transition and evolves the resulting glass arbitrarily close to jamming, approximating an adiabatic state following [18].”
Jammed hard-particle packings: From Kepler to Bernal and beyond (2010, background): “…insight into liquid and glassy states of matter as well as phase behavior in lower dimensions (Adda-Bedia et al., 2008; Frisch and Percus, 1999; van Meel et al., 2009; Parisi and Slanina, 2000; Parisi and Zamponi, 2006, 2010; Rohrmann and Santos, 2007; Skoge et al., 2006; van Meel et al., 2009).”
Theoretical perspective on the glass transition and amorphous materials (2010, background): “Thus, when accurate results are sought, the problem might well become technically quite involved (Parisi and Zamponi, 2010).”
Hyperuniform states of matter (2018, background): “Understanding the characteristics of jammed particle packings provides basic insights into the structure and bulk properties of crystals, glasses, and granular media and selected aspects of biological systems [199, 245].”