Benjamin Guiselin, Ludovic Berthier, Gilles Tarjus
SciPost Phys. 12, 091 (2022) ·
published 14 March 2022
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We study the statistical mechanics of supercooled liquids when the system evolves at a temperature $T$ with a field $\epsilon$ linearly coupled to its overlap with a reference configuration of the same liquid sampled at a temperature $T_0$. We use mean-field theory to fully characterize the influence of the reference temperature $T_0$, and we mainly study the case of a fixed, low-$T_0$ value in computer simulations. We numerically investigate the extended phase diagram in the $(\epsilon,T)$ plane of model glass-forming liquids in spatial dimensions $d=2$ and $d=3$, relying on umbrella sampling and reweighting techniques. For both $2d$ and $3d$ cases, a similar phenomenology with nontrivial thermodynamic fluctuations of the overlap is observed at low temperatures, but a detailed finite-size analysis reveals qualitatively distinct behaviors. We establish the existence of a first-order transition line for nonzero $\epsilon$ ending in a critical point in the universality class of the random-field Ising model (RFIM) in $d=3$. In $d=2$ instead, no phase transition is found in large enough systems at least down to temperatures below the extrapolated calorimetric glass transition temperature $T_g$. Our results confirm that glass-forming liquid samples of limited size display the thermodynamic fluctuations expected for finite systems undergoing a random first-order transition. They also support the relevance of the physics of the RFIM for supercooled liquids, which may then explain the qualitative difference between $2d$ and $3d$ glass-formers.
Daniele Coslovich, Andrea Ninarello, Ludovic Berthier
SciPost Phys. 7, 077 (2019) ·
published 6 December 2019
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We study the equilibrium statistical properties of the potential energy
landscape of several glass models in a temperature regime so far inaccessible
to computer simulations. We show that unstable modes of the stationary points
undergo a localization transition in real space close to the mode-coupling
crossover temperature determined from the dynamics. The concentration of
localized unstable modes found at low temperature is a non-universal, finite
dimensional feature not captured by mean-field glass theory. Our analysis
reconciles, and considerably expands, previous conflicting numerical results
and provides a characteristic temperature for glassy dynamics that
unambiguously locates the mode-coupling crossover.
SciPost Phys. 3, 027 (2017) ·
published 12 October 2017
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We numerically study the jamming transition of frictionless polydisperse
spheres in three dimensions. We use an efficient thermalisation algorithm for
the equilibrium hard sphere fluid and generate amorphous jammed packings over a
range of critical jamming densities that is about three times broader than in
previous studies. This allows us to reexamine a wide range of structural
properties characterizing the jamming transition. Both isostaticity and the
critical behavior of the pair correlation function hold over the entire range
of jamming densities. At intermediate length scales, we find a weak, smooth
increase of bond orientational order. By contrast, distorted icosahedral
structures grow rapidly with increasing the volume fraction in both fluid and
jammed states. Surprisingly, at large scale we observe that denser jammed
states show stronger deviations from hyperuniformity, suggesting that the
enhanced amorphous ordering inherited from the equilibrium fluid competes with,
rather than enhances, hyperuniformity. Finally, finite size fluctuations of the
critical jamming density are considerably suppressed in the denser jammed
states, indicating an important change in the topography of the potential
energy landscape. By considerably stretching the amplitude of the critical
"J-line", our work disentangles physical properties at the contact scale that
are associated with jamming criticality, from those occurring at larger length
scales, which have a different nature.
