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  • Letter
  • Open Access

Minimal model of universal viscous liquid dynamics

Ulf R. Pedersen*

  • “Glass and Time”, IMFUFA, Department of Science and Environment, Roskilde University, P.O. Box 260, DK-4000 Roskilde, Denmark

  • *Contact author: ulf@urp.dk
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Phys. Rev. Research 8, L032028 – Published 21 August, 2026

DOI: https://doi.org/10.1103/tkt1-gbyx

Abstract

When liquids are cooled and crystallization is avoided, their dynamics slow dramatically and the material eventually solidifies into an amorphous glass. Experiments show that chemically distinct glass-forming liquids share universal features in both the spectral shape and the temperature dependence of the primary structural relaxation. We introduce Randium, a generic, energetically coarse-grained minimal model of viscous liquids. The model, inspired by results from atomistic molecular-dynamics simulations, is implemented on a two-dimensional lattice with Gaussian-distributed nearest-neighbor interactions. Temperature is the only control parameter, and at low temperatures, dynamic facilitation and dynamical heterogeneity emerge from simple nearest-neighbor rearrangements. The relaxation spectra obey time-temperature superposition, and they reproduce shapes observed experimentally for chemically distinct systems. The temperature dependence of the structural-relaxation time follows parabolic scaling, and the relaxation time grows exponentially with the heterogeneity length scale. The mean-squared displacement collapses onto the universal master curve of the random barrier model. The absence of elasticity-induced facilitation in Randium shows that this is not required for universal viscous-liquid dynamics. Other explanations for universal relaxation are discussed in light of Randium.

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Phys. Rev. Research 8, L032028– Published 21 August, 2026
  • Received 1 December 2025
  • Accepted 4 August 2026
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