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, , with D and the diffusion constant of the probe particle and the relaxation time of the model liquid, respectively, and where 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.
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28 August 2017
Research Article|
August 28 2017
Study of the upper-critical dimension of the East model through the breakdown of the Stokes-Einstein relation
Soree Kim;
Soree Kim
a)
1
Department of Chemistry, Seoul National University
, Seoul 08826, South Korea
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Dayton G. Thorpe;
Dayton G. Thorpe
a)
2
Department of Chemistry, University of California
, Berkeley, California 94720, USA
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Chanwoo Noh
;
Chanwoo Noh
1
Department of Chemistry, Seoul National University
, Seoul 08826, South Korea
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Juan P. Garrahan
;
Juan P. Garrahan
3
School of Physics and Astronomy, University of Nottingham
, Nottingham NG7 2RD, United Kingdom
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David Chandler;
David Chandler
b)
2
Department of Chemistry, University of California
, Berkeley, California 94720, USA
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YounJoon Jung
YounJoon Jung
c)
1
Department of Chemistry, Seoul National University
, Seoul 08826, South Korea
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a)
S. Kim and D. G. Thorpe contributed equally to this work.
b)
Deceased 18 April 2017.
c)
Electronic mail: yjjung@snu.ac.kr
J. Chem. Phys. 147, 084504 (2017)
Article history
Received:
May 15 2017
Accepted:
August 04 2017
Citation
Soree Kim, Dayton G. Thorpe, Chanwoo Noh, Juan P. Garrahan, David Chandler, YounJoon Jung; Study of the upper-critical dimension of the East model through the breakdown of the Stokes-Einstein relation. J. Chem. Phys. 28 August 2017; 147 (8): 084504. https://doi.org/10.1063/1.4999791
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