Low-temperature properties of crystalline solids can be understood using harmonic perturbations around a perfect lattice, as in Debye's theory. Low-temperature properties of amorphous solids, however, strongly depart from such descriptions, displaying enhanced transport, activated slow dynamics across energy barriers, excess vibrational modes with respect to Debye's theory (i.e., a boson peak), and complex irreversible responses to small mechanical deformations. These experimental observations indirectly suggest that the dynamics of amorphous solids becomes anomalous at low temperatures. Here, we present direct numerical evidence that vibrations change nature at a well-defined location deep inside the glass phase of a simple glass former. We provide a real-space description of this transition and of the rapidly growing time-and lengthscales that accompany it. Our results provide the seed for a universal understanding of low-temperature glass anomalies within the theoretical framework of the recently discovered Gardner phase transition.glass transition | disordered solids | Gardner transition | computer simulations | hard spheres U nderstanding the nature of the glass transition, which describes the gradual transformation of a viscous liquid into an amorphous solid, remains an open challenge in condensed matter physics (1, 2). As a result, the glass phase itself is not well understood either. The main challenge is to connect the localized, or "caged," dynamics that characterizes the glass transition to the low-temperature anomalies that distinguish amorphous solids from their crystalline counterparts (3-7). Recent theoretical advances, building on the random first-order transition approach (8), have led to an exact mathematical description of both the glass transition and the amorphous phases of hard spheres in the mean-field limit of infinite-dimensional space (9). A surprising outcome has been the discovery of a novel phase transition inside the amorphous phase, separating the localized states produced at the glass transition from their inherent structures. This Gardner transition (10), which marks the emergence of a fractal hierarchy of marginally stable glass states, can be viewed as a glass transition deep within a glass, at which vibrational motion dramatically slows down and becomes spatially correlated (11). Although these theoretical findings promise to explain and unify the emergence of low-temperature anomalies in amorphous solids, the gap remains wide between mean-field calculations (9, 11) and experimental work. Here, we provide direct numerical evidence that vibrational motion in a simple 3D glass-former becomes anomalous at a well-defined location inside the glass phase. In particular, we report the rapid growth of a relaxation time related to cooperative vibrations, a nontrivial change in the probability distribution function of a global order parameter, and the rapid growth of a correlation length. We also relate these findings to observed anomalies in low-temperature laboratory glasses. These re...

We report a high-precision finite-size scaling study of the critical behavior of the three-dimensional Ising Edwards-Anderson model (the Ising spin glass). We have thermalized lattices up to L = 40 using the Janus dedicated computer. Our analysis takes into account leading-order corrections to scaling. We obtain T c = 1.1019(29) for the critical temperature, ν = 2.562(42) for the thermal exponent, η = −0.3900(36) for the anomalous dimension, and ω = 1.12(10) for the exponent of the leading corrections to scaling. Standard (hyper)scaling relations yield α = −5.69(13), β = 0.782(10), and γ = 6.13(11). We also compute several universal quantities at T c .

-Temperature chaos has often been reported in literature as a rare-event driven phenomenon. However, this fact has always been ignored in the data analysis, thus erasing the signal of the chaotic behavior (still rare in the sizes achieved) and leading to an overall picture of a weak and gradual phenomenon. On the contrary, our analysis relies on a large-deviations functional that allows to discuss the size dependencies. In addition, we had at our disposal unprecedentedly large configurations equilibrated at low temperatures, thanks to the Janus computer. According to our results, when temperature chaos occurs its effects are strong and can be felt even at short distances.Temperature chaos (TC) refers to the complete reorganization of the equilibrium configurations by the slightest change in temperature. This effect was initially predicted in spin glasses (SG) [1][2][3] but it is expected as well in other glassy materials such as polymers [4,5] or vortex glasses [6].An experimental measurement of TC is still missing. The main difficulty arises from the nonequilibrium nature of the experimental glass: since chaos is an equilibrium property, it is not clear how to detect it in nonequilibrium responses (such as the aging magnetic susceptibility [7], for instance). Nevertheless, TC is often regarded as the origin of the anomalous response of glasses in temperature cycles, and in particular, of the spectacular rejuvenation (and memory) effects found in SG [8] (however, see [9,10] for a dissenting view). Although memory and rejuvenation have been also identified in colloids [11], polymers [12,13], ferro-electrics [14,15], and in the ferromagnetic phase of disordered magnetic alloys [16], these are tiny effects as compared to their SG counterpart. Thus, experiments suggest that TC is peculiar in SG.Unfortunately, a rigorous theoretical description of TC has been achieved only for directed polymers in random media in 1+1 dimensions [4,5]. Coming to SG, the analytical work has been mostly concerned with meanfield (MF) approximations. Some accidental cancellations make TC anomalously weak in the SherringtonKirkpatrick model [17] (the standard model in MF approximations), which favored a long controversy about its very existence [18][19][20][21][22][23][24][25]. Only recently the question has been answered in the positive, by the explicit computation of a large-deviation functional (i.e. the free-energy cost of constraining a SG to have similar spin configurations at two temperatures below the critical one, T 1 , T 2 < T c ) [25,26]. A large-deviation functional will play as well a crucial role in this work.Besides, the theoretical work in non MF models is restricted to equilibrium numerical simulations [27][28][29][30][31]. Data were analyzed using a scaling picture (valid for polymers), in which a characteristic length-scale should appear ξ C (T 1 , T 2 ) in the comparison of the system at two temperatures T 1 , T 2 < T c [32,33]. Spin configurations at temperatures T 1 and T 2 would be similar (different), if co...