Impact of jamming criticality on low-temperature anomalies in structural glasses

Abstract

We present a mechanism for the anomalous behavior of the specific heat in low-temperature amorphous solids. The analytic solution of a mean-field model belonging to the same universality class as high-dimensional glasses, the spherical perceptron, suggests that there exists a cross-over temperature above which the specific heat scales linearly with temperature, while below it, a cubic scaling is displayed. This relies on two crucial features of the phase diagram: (i) the marginal stability of the free-energy landscape, which induces a gapless phase responsible for the emergence of a power-law scaling; and (ii) the vicinity of the classical jamming critical point, as the cross-over temperature gets lowered when approaching it. This scenario arises from a direct study of the thermodynamics of the system in the quantum regime, where we show that, contrary to crystals, the Debye approximation does not hold.

Emergent solidity of amorphous materials as a consequence of mechanical self-organisation

“…Marginal stability of amorphous solids is predicted to root in the Gardner transition from a normal glass phase into a marginally stable one 31,32 , which leads to hierarchical dynamics at low temperatures much more complex than simple vibrations expected from the original PEL picture 33 . Consequently, the marginal stability intrinsically cuts off the direct link between properties of amorphous solids at zero and finite temperatures 34,35 , although the concept of marginal stability may not be universally valid in a strict sense for all amorphous solids 36 . Thus, we may conclude that there is actually no solid base to deduce the properties of thermal amorphous solids directly from the IS.…”

Quantum Jamming: Critical Properties of a Quantum Mechanical Perceptron

“…The purpose of this paper is precisely to show that, in a model that describes the limit d → ∞ of the jamming transition, quantum mechanical effects change the nature of the critical phase radically. This paper complements the semiclassical analysis of [14], in which the corrections to the classical quantities were computed at O( ), and a linear specific heat C V (T ) was found. In this paper we show that the limits → 0 and T → 0 do not commute at the jamming point, and that for non-zero one gets different critical exponents, independent of the temperature, and that C V (T ) ∼ e −∆/T .…”

“…bits) map naturally to Ising spin glasses (the disorder arising due to the sampling of instances from a large ensemble), CSP defined in terms of continuous variables [6,7] have shown several similarities and a deep connection with the sphere-packing problem and their jamming transition (i.e. configurational glasses) [8][9][10][11][12][13][14]. In both problems, substituting a classical spinflip dynamics with a transverse field or the free particle kinetic term with its quantized counterpart can have profound consequences, both at the theoretical and the practical level.…”

“…We want to compute the partition function Z = Tr(e −βH ), the free energy F = −β −1 ln Z, and then take a quenched disorder average. After following the procedure in [14,36], the quenched free energy is expressed in terms of the autocorrelation function G(t − s) ≡ r(t)r(s) r , r(t) being a one-dimensional, β -periodic auxiliary process and…”

“…The internal energy per degree of freedom u (see [14]) is independent of β, like q, already at α 1, but it depends on the number of Trotter slices N . Extrapolating the data for N → ∞ we obtain the result in Fig.…”