Abstract
Understanding the fundamental nature of the glass transition and amorphous solids is at the core of a large research effort. The theoretical description of glassy solids remains mainly phe- nomenological. This work explores the hypothesis that a new amorphous phase of matter naturally explains their physical properties. We analyze the thermodynamics of glasses in the limit of large dimensions. This exact mean-field theory predicts two glassy phases, ‘simple’ and ‘marginally stable’, separated by a Gardner transition. We find that glasses are marginally stable in a wide range of physical conditions, covering regimes relevant to describe granular matter, foams, emul- sions, hard and soft colloids, and molecular glasses. We confront our theoretical predictions to three-dimensional numerical simulations. We develop an efficient numerical scheme which creates well-relaxed glasses. Colloidal and granular glasses are found to be marginally stable: they evolve in a hierarchical landscape, and present delocalized low-lying excitations. Temperature cycles in this regime give rise to rejuvenation and memory effects, previously observed in spin glasses. In contrast, the behavior of molecular glasses is governed by localized two level systems, whose low- temperature tunneling properties are also analyzed. We investigate the role of the configurational entropy in the glassy dynamical slowdown accompanying glass formation. We measure the config- urational entropy in extremely supercooled liquids, and assess thermodynamic theories of the glass transition.