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Ref Arxiv: 2207.07715
DOI: 10.1063/5.0126437
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We discuss pressure computations for the hard-disk model performed since 1953 and compare them to the results that we obtain with a powerful event-chain Monte Carlo and a massively parallel Metropolis algorithm. Like other simple models in the sciences, such as the Drosophila model of biology, the hard-disk model has needed monumental efforts to be understood. In particular, we argue that the difficulty of estimating the pressure has not been fully realized in the decades-long controversy over the hard-disk phase-transition scenario. We present the physics of the hard-disk model, the definition of the pressure and its unbiased estimators, several of which are new. We further treat different sampling algorithms and crucial criteria for bounding mixing times in the absence of analytical predictions. Our definite results for the pressure, for up to one million disks, may serve as benchmarks for future sampling algorithms. A synopsis of hard-disk pressure data as well as different versions of the sampling algorithms and pressure estimators are made available in an open-source repository.

Commentaires: 21 pages, 13 figures, open-source repository

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Ref Arxiv: 2207.00491
DOI: 10.1103/PhysRevX.12.041028
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We combine the swap Monte Carlo algorithm to long multi-CPU molecular dynamics simulations to analyse the equilibrium relaxation dynamics of model supercooled liquids over a time window covering ten orders of magnitude for temperatures down to the experimental glass transition temperature $T_g$. The analysis of \rev{several} time correlation functions coupled to spatio-temporal resolution of particle motion allow us to elucidate the nature of the equilibrium dynamics in deeply supercooled liquids. We find that structural relaxation starts at early times in rare localised regions characterised by a waiting time distribution that develops a power law near $T_g$. At longer times, relaxation events accumulate with increasing probability in these regions as $T_g$ is approached. This accumulation leads to a power-law growth of the linear extension of relaxed domains with time with a large, temperature-dependent dynamic exponent. Past the average relaxation time, unrelaxed domains slowly shrink with time due to relaxation events happening at their boundaries. Our results provide a complete microscopic description of the particle motion responsible for key experimental signatures of glassy dynamics, from the shape and temperature evolution of relaxation spectra to the core features of dynamic heterogeneity. They also provide a microscopic basis to understand the emergence of dynamic facilitation in deeply supercooled liquids and allow us to critically reassess theoretical descriptions of the glass transition.

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Ref Arxiv: 2207.14204
DOI: 10.13036/17533562.63.5.15
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Glass is everywhere. We use and are surrounded by glass objects which make tangible the reality of glass as a distinct state of matter. Yet, glass as we know it is usually obtained by cooling a liquid sufficiently rapidly below its melting point to avoid crystallisation. The viscosity of this supercooled liquid increases by many orders of magnitude upon cooling, until the liquid becomes essentially arrested on experimental timescales below the ``glass transition'' temperature. From a structural viewpoint, the obtained glass still very much resembles the disordered liquid, but from a mechanical viewpoint, it is as rigid as an ordered crystal. Does glass qualify as a separate state of matter? We provide a pedagogical perspective on this question using basic statistical mechanical concepts. We recall the definitions of states of matter and of phase transitions between them. We review recent theoretical results suggesting why and how an ``ideal glass'' can indeed be defined as a separate equilibrium state of matter. We discuss recent success of computer simulations trying to analyse this glass state. We close with some experimental perspectives.

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Ref Arxiv: 2209.10473
DOI: 10.1103/PhysRevLett.129.228004
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DOI: 10.1103/PhysRevMaterials.6.085601
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