Viscous liquid dynamics modeled as random walks within overlapping hyperspheres

The hypersphere model is a simple one-parameter model of the potential-energy landscape of viscous liquids, which is defined as a percolating system of same-radius hyperspheres randomly distributed in R^{3N}, in which N is the number of particles. We study random walks within overlapping hyperspheres above the percolation threshold in 12 to 45 dimensions, utilizing an algorithm for on-the-fly placement of the hyperspheres in conjunction with the kinetic Monte Carlo method. We find behavior typical of viscous liquids; decreasing the hypersphere density (corresponding to decreasing the temperature) leads to a slowing down of the dynamics by many orders of magnitude. The shape of the mean-square displacement as a function of time is found to be similar to that of the Kob-Andersen binary Lennard-Jones mixture and the random barrier model, which predicts well the frequency-dependent fluidity of nine glass-forming liquids of different chemistry [Bierwirth et al., Phys. Rev. Lett. 119, 248001 (2017)0031-900710.1103/PhysRevLett.119.248001].