Study of the upper-critical dimension of the East model through the breakdown of the Stokes-Einstein relation
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 formi...
| Main Authors: | , , , , , |
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| Format: | Article |
| Published: |
American Institute of Physics
2017
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| Online Access: | https://eprints.nottingham.ac.uk/46284/ |
| _version_ | 1848797295137521664 |
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| author | Kim, Soree Thorpe, Dayton G. Noh, Chanwoo Garrahan, Juan P. Chandler, David Jung, Chanwoo |
| author_facet | Kim, Soree Thorpe, Dayton G. Noh, Chanwoo Garrahan, Juan P. Chandler, David Jung, Chanwoo |
| author_sort | Kim, Soree |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T20:01:36Z |
| format | Article |
| id | nottingham-46284 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T20:01:36Z |
| publishDate | 2017 |
| publisher | American Institute of Physics |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-462842020-05-04T19:02:28Z https://eprints.nottingham.ac.uk/46284/ Study of the upper-critical dimension of the East model through the breakdown of the Stokes-Einstein relation Kim, Soree Thorpe, Dayton G. Noh, Chanwoo Garrahan, Juan P. Chandler, David Jung, Chanwoo 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. American Institute of Physics 2017-08-28 Article PeerReviewed Kim, Soree, Thorpe, Dayton G., Noh, Chanwoo, Garrahan, Juan P., 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 http://aip.scitation.org/doi/10.1063/1.4999791 doi:10.1063/1.4999791 doi:10.1063/1.4999791 |
| spellingShingle | Kim, Soree Thorpe, Dayton G. Noh, Chanwoo Garrahan, Juan P. Chandler, David Jung, Chanwoo Study of the upper-critical dimension of the East model through the breakdown of the Stokes-Einstein relation |
| title | Study of the upper-critical dimension of the East model through the breakdown of the Stokes-Einstein relation |
| title_full | Study of the upper-critical dimension of the East model through the breakdown of the Stokes-Einstein relation |
| title_fullStr | Study of the upper-critical dimension of the East model through the breakdown of the Stokes-Einstein relation |
| title_full_unstemmed | Study of the upper-critical dimension of the East model through the breakdown of the Stokes-Einstein relation |
| title_short | Study of the upper-critical dimension of the East model through the breakdown of the Stokes-Einstein relation |
| title_sort | study of the upper-critical dimension of the east model through the breakdown of the stokes-einstein relation |
| url | https://eprints.nottingham.ac.uk/46284/ https://eprints.nottingham.ac.uk/46284/ https://eprints.nottingham.ac.uk/46284/ |