Study of the upper-critical dimension of the East model through the breakdown of the Stokes-Einstein relation

Kim, Soree and Thorpe, Dayton G. and Noh, Chanwoo and Garrahan, Juan P. and Chandler, David and Jung, Chanwoo (2017) Study of the upper-critical dimension of the East model through the breakdown of the Stokes-Einstein relation. Journal of Chemical Physics, 147 (8). 084504-1-084504-7. ISSN 1089-7690

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Abstract

We investigate the dimensional dependence of dynamical fluctuations related to dynamic heterogeneity in supercooled liquid systems using kinetically constrained models. The d-dimensional spin-facilitated East model with embedded probe particles is used as a representative super-Arrhenius glass forming system. We examine the existence of an upper critical dimension in this model by considering decoupling of transport rates through an effective fractional Stokes-Einstein relation, D∼τ−1+ωD∼τ−1+ω, with D and ττ the diffusion constant of the probe particle and the relaxation time of the model liquid, respectively, and where ω>0ω>0 encodes the breakdown of the standard Stokes-Einstein relation. To the extent that decoupling indicates non-mean-field behavior, our simulations suggest that the East model has an upper critical dimension at least above d = 10 and argue that it may actually be infinite. This result is due to the existence of hierarchical dynamics in the East model in any finite dimension. We discuss the relevance of these results for studies of decoupling in high dimensional atomistic models.

Item Type: Article
Schools/Departments: University of Nottingham, UK > Faculty of Science > School of Physics and Astronomy
Identification Number: 10.1063/1.4999791
Depositing User: Eprints, Support
Date Deposited: 14 Sep 2017 11:00
Last Modified: 14 Oct 2017 08:48
URI: http://eprints.nottingham.ac.uk/id/eprint/46284

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