Glass and Jamming Transitions: From Exact Results to Finite-Dimensional Descriptions

By Patrick Charbonneau, Jorge Kurchan, Giorgio Parisi, Pierfrancesco Urbani, Francesco Zamponi. 2016

296 citations recorded by the source corpus.

Despite decades of work, gaining a first-principle understanding of amorphous materials remains an extremely challenging problem. However, recent theoretical breakthroughs have led to the formulation of an exact solution in the mean-field limit of infinite spatial dimension, and numerical simulations have remarkably confirmed the dimensional robustness of some of the predictions. This review describes these latest advances. More specifically, we consider the dynamical and thermodynamic descriptions of hard spheres around the dynamical, Gardner and jamming transitions. Comparing mean-field predictions with the finite-dimensional simulations, we identify robust aspects of the description and uncover its more sensitive features. We conclude with a brief overview of ongoing research.

Subfields: Biomedical Engineering, Condensed Matter Physics, Materials Chemistry

View Paper: https://www.semanticscholar.org/paper/4884168e3e62099350c8648b11c2320b3899896f

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Biomedical Engineering

In Condensed Matter Physics

In Materials Chemistry

Citations in the corpus

Universality of the SAT-UNSAT (jamming) threshold in non-convex continuous constraint satisfaction problems (2017, background): “…description of the glassy phases of high-dimensional sphere systems and the discovery that universal predictions at jamming match ﬁnite dimensional observations [ 1 ] has re-newed the interest in the statistical physics of random constraint satisfaction problems (CSP) with continuous variables.”
Edwards Statistical Mechanics for Jammed Granular Matter (2016, background): “Edwards statistical mechanics thus captures key features of the jamming phenomenology, a fact that is increasingly being recognized (Charbonneau et al., 2017; Sharma et al., 2016).”