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

Jung, Younjoon; Kim, Soree; Thorpe, Dayton G.; Noh, Chanwoo; Garrahan, Juan P.; Chandler, David

Abstract

© 2017 Author(s). 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+ω, with D and τ the diffusion constant of the probe particle and the relaxation time of the model liquid, respectively, and where ω>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.

Citation

Jung, Y., Kim, S., Thorpe, D. G., Noh, C., Garrahan, J. P., & Chandler, D. (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), https://doi.org/10.1063/1.4999791

• Journal Article Type: Article
• Acceptance Date: Aug 4, 2017
• Online Publication Date: Dec 28, 2017
• Publication Date: Aug 28, 2017
• Deposit Date: Sep 14, 2017
• Publicly Available Date: Sep 14, 2017
• Journal: Journal of Chemical Physics
• Print ISSN: 0021-9606
• Electronic ISSN: 1089-7690
• Publisher: American Institute of Physics
• Peer Reviewed: Peer Reviewed
• Volume: 147
• Issue: 8
• DOI: https://doi.org/10.1063/1.4999791
• Public URL: https://nottingham-repository.worktribe.com/output/879320
• Publisher URL: http://aip.scitation.org/doi/10.1063/1.4999791
• Contract Date: Sep 14, 2017