The physics of the glass transition and amorphous materials continues to attract the attention of a wide research community after decades of effort. Supercooled liquids and glasses have been studied numerically since the advent of molecular dynamics and Monte Carlo simulations, and computer studies have greatly enhanced both experimental discoveries and theoretical developments. In this Review, we provide a modern perspective on this area. We describe the need to go beyond canonical methods when studying the glass transition — a problem that is notoriously difficult in terms of timescales, length scales and physical observables. We summarize recent algorithmic developments to achieve enhanced sampling and faster equilibration by using replica-exchange methods, cluster and swap Monte Carlo algorithms, and other techniques. We then review some major advances afforded by these tools regarding the statistical mechanical description of the liquid-to-glass transition, and the mechanical, vibrational and thermal properties of the glassy solid.
Simulations of glass-forming systems suffer from the rapidly growing relaxation times near the glass transition, which historically have limited simulations to the regime of very mild supercooling.
A variety of methods, including simulated tempering methods and cluster Monte Carlo approaches, have been developed to deal with issues relating to slow equilibration.
More recently, swap Monte Carlo methods, which augment standard local moves with swaps between particles that may be physically distant, have been shown to enable remarkably efficient equilibration in certain models of glass-forming systems.
The equilibration speed-up afforded by swap Monte Carlo makes it possible to study glassy properties and behaviours that were previously out of reach, such as the nature of low-energy excitations in well-annealed glasses, and the brittle-to-ductile transition.
Swap Monte Carlo has opened new vistas for the study of the behaviour of glassy systems, but new approaches for the simulation of dynamical behaviour as well as the equilibration of more complex glass-formers are still needed.
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This work was supported by grants from the Simons Foundation (454933 to L.B., 454951 to D.R.R.) and by a Visiting Professorship from the Leverhulme Trust (VP1-2019-029, LB). The authors thank all of the members of the Simons Foundation Collaboration on ‘Cracking the Glass Problem’ for six-plus years of stimulating discussions.
The authors declare no competing interests.
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Berthier, L., Reichman, D.R. Modern computational studies of the glass transition. Nat Rev Phys 5, 102–116 (2023). https://doi.org/10.1038/s42254-022-00548-x