Universal behaviour of the glass and the jamming transitions in finite dimensions for hard spheres

Abstract

We investigate the glass and the jamming transitions of hard spheres in finite dimensions d, through a revised cell theory, that combines the free volume and the Random First Order Theory (RFOT). Recent results show that in infinite dimension the ideal glass transition and jamming transitions are distinct, while based on our theory we argue that they indeed coincide for finite d. As a consequence, jamming results into a percolation transition described by RFOT, with a static length diverging with exponent ν = 2/d, which we verify through finite size scaling, and standard critical exponents α = 0, β = 0 and γ = 2 independent on d.

Exploring the jamming transition over a wide range of critical densities

“…This conclusion, based on our numerical findings, also directly contradicts an opposite theoretical prediction recently made in Ref. [103].…”

“…The obtained ν's are slightly different from previous reports [5,114]. Note that ν for φ fluid = 0.4 is compatible with very recent numerical work [103]. However, we do not wish to discuss these values quantitatively because ν might be protocol or algorithm dependent, and corrections to scaling should be included before drawing any strong conclusions [112].…”

“…In a recent numerical study of polydisperse hard spheres [79], we demonstrated the growth of non-trivial static "point-to-set" correlations, which are at the core of thermodynamic pictures of the glass transition [121]. It has been suggested that such "amorphous order" could be identified with hyperuniformity [100,103], although this link has been questioned [25]. Our results cast further doubts on this argument: point-to-set correlations grow as the volume fraction increases, while hyperuniform behavior is suppressed.…”

Hyperuniform states of matter

“…Understanding structural and physical properties of a system as it approaches a hyperuniform state or whether near hyperuniformity is signaling crucial large-scale structural changes in a system will be shown to be fundamentally important and is expected to lead to new insights about condensed phases of matter. Indeed, the hyperuniformity concept has suggested a "nonequilibrium index" for glasses [40] as well as new correlation functions from which one can extract relevant growing length scales as a function of temperature as a liquid is supercooled below its glass transition temperature [40,103], a problem of intense interest in the glass physics community [22,[104][105][106][107][108][109][110]].…”

Dynamic Measure of Hyperuniformity and Nonhyperuniformity in Heterogeneous Media via the Diffusion Spreadability

“…II B for exact mathematical definitions. Hyperuniformity is an emerging field, playing vital roles in a number of fundamental and applied contexts, including glass formation [19,20], jamming [21][22][23][24][25], rigidity [26,27], bandgap structures [28][29][30], biology [31,32], localization of waves and excitations [33][34][35], self-organization [36][37][38], fluid dynamics [39,40], quantum systems [41][42][43][44][45], random matrices [43,46,47] and pure mathematics [48][49][50][51][52]. Because disordered hyperuniform two-phase media are states of matter that lie between a crystal and a typical liquid, they can be endowed with novel properties [12,18,[53][54][55][56][57][58][59][60][61][62][63]…”