Zero-temperature glass transition in two dimensions

Berthier, Ludovic; Charbonneau, Patrick; Ninarello, Andrea; Ozawa, Masakuni; Yaida, Sho

doi:10.1038/s41467-019-09512-3

Cited by 98 publications

(112 citation statements)

References 75 publications

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“…In the vicinity of T g , ξ PTS is actually small, only a few molecular diameters [34,37,38]. As a consequence of new simulational methods (the swap algorithm [9,38]) it has now become possible to study ξ PTS at temperatures well-below T g where indeed it becomes somewhat longer. According to RFOT theory it diverges as T → T K , but if the discontinuous transition is removed by fluctuations around the mean-field solution and the transition is avoided, the correlation length will not actually diverge, just as was seen in the Migdal-Kadanoff RG procedure [23,26].…”

Section: Discussionmentioning

confidence: 99%

Possible instability of one-step replica symmetry breaking in p -spin Ising models outside mean-field theory

Yeo

Moore

2020

Phys. Rev. E

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The fully-connected Ising p-spin model has for p > 2 a discontinuous phase transition from the paramagnetic phase to a stable state with one-step replica symmetry breaking (1RSB). However, simulations in three dimension do not look like these mean-field results and have features more like those which would arise with full replica symmetry breaking (FRSB). To help understand how this might come about we have studied in the fully connected p-spin model the state of two-step replica symmetry breaking (2RSB). It has a free energy degenerate with that of 1RSB, but the weight of the additional peak in P (q) vanishes. We expect that the state with full replica symmetry breaking (FRSB) is also degenerate with that of 1RSB. We suggest that finite size effects will give a nonvanishing weight to the FRSB features, as also will fluctuations about the mean-field solution. Our conclusion is that outside the fully connected model in the thermodynamic limit, FRSB is to be expected rather than 1RSB. arXiv:1911.02719v2 [cond-mat.dis-nn]

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Section: Discussionmentioning

confidence: 99%

Possible instability of one-step replica symmetry breaking in p -spin Ising models outside mean-field theory

Yeo

Moore

2020

Phys. Rev. E

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“…To test this hypothesis we seek to substantially increase the stability of our computer glasses, and by doing so to suppress the occurrence and spatial extent of soft quasilocalized modes in a physical manner. To this aim we employ the Swap Monte Carlo method and an optimized glass forming model [21], which was recently shown to be very efficient in 2D [38], allowing for extremely deep supercooling. Details about our simulations and employed methods are provided in Appendix A.…”

Section: The Generalized-rayleigh Scaling Depends On Glass Stabilitymentioning

confidence: 99%

Wave attenuation in glasses: Rayleigh and generalized-Rayleigh scattering scaling

Moriel

Kapteijns

Rainone

et al. 2019

The Journal of Chemical Physics

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The attenuation of long-wavelength phonons (waves) by glassy disorder plays a central role in various glass anomalies, yet it is neither fully characterized, nor fully understood. Of particular importance is the scaling of the attenuation rate Γ(k) with small wavenumbers k → 0 in the thermodynamic limit of macroscopic glasses. Here we use a combination of theory and extensive computer simulations to show that the macroscopic low-frequency behavior emerges at intermediate frequencies in finite-size glasses, above a recently identified crossover wavenumber k † , where phonons are no longer quantized into bands. For k < k † , finite-size effects dominate Γ(k), which is quantitatively described by a theory of disordered phonon bands. For k > k † , we find that Γ(k) is affected by the number of quasilocalized nonphononic excitations, a generic signature of glasses that feature a universal density of states. In particular, we show that in a frequency range in which this number is small, Γ(k) follows a Rayleigh scattering scaling ∼ kd +1 (d is the spatial dimension), and that in a frequency range in which this number is sufficiently large, the recently observed generalized-Rayleigh scaling of the form ∼ kd +1 log(k0/k) emerges (k0 > k † is a characteristic wavenumber). Our results suggest that macroscopic glasses -and, in particular, glasses generated by conventional laboratory quenches that are known to strongly suppress quasilocalized nonphononic excitations -exhibit Rayleigh scaling at the lowest wavenumbers k and a crossover to generalized-Rayleigh scaling at higher k. Some supporting experimental evidence from recent literature is presented.

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“…For instance, the static hexatic length scale grows as the dynamical length scale increases and diverges at the MCT point, in polydisperse discs [61,62]. Differently, the amorphous length scale quantified by the point-to-set length scale only grows mildly in the supercooled region [58,59,63], possibly diverging only at zero temperature [64].…”

Section: F Spatial Correlation and Length Scalesmentioning

confidence: 99%

Dynamics in two-dimensional glassy systems of crowded Penrose kites

Hou

et al. 2019

Phys. Rev. Materials

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We investigate the translational and rotational relaxation dynamics of a crowded two-dimensional system of monodisperse Penrose kites, in which crystallization, quasi-crystallization and nematic ordering are suppressed, from low to high area fractions along the metastable ergodic fluid branch. First, we demonstrate a decoupling between both the translational and the rotational diffusion coefficients and the relaxation time: the diffusivities are not inversely proportional to the relaxation time, neither in the low-density normal liquid regime nor in the high-density supercooled regime. Our simulations reveal that this inverse proportionality breaks in the normal liquid regime due to the Mermin-Wagner long-wavelength fluctuations and in the supercooled regime due to the dynamical heterogeneities. We then show that dynamical heterogeneities are mainly spatial for translational degrees of freedom and temporal for rotational ones, that there is no correlation between the particles with largest translational and rotational displacements, and that different dynamical length scales characterize the translational and the rotational motion. Hence, despite the translational and the rotational glass-transition densities coincide, according to a mode-coupling fit, translations and rotations appear to decorrelate via different dynamical processes.

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Zero-temperature glass transition in two dimensions

Cited by 98 publications

References 75 publications

Possible instability of one-step replica symmetry breaking in p -spin Ising models outside mean-field theory

Possible instability of one-step replica symmetry breaking in p -spin Ising models outside mean-field theory

Wave attenuation in glasses: Rayleigh and generalized-Rayleigh scattering scaling

Dynamics in two-dimensional glassy systems of crowded Penrose kites

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