Department of Chemistry, Seoul National University, Seoul 08826, South Korea.
Department of Chemistry, University of California, Berkeley, California 94720, USA.
J Chem Phys. 2017 Aug 28;147(8):084504. doi: 10.1063/1.4999791.
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, 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.
我们使用动力学约束模型研究了与过冷液体系统中动态非均匀性相关的动力学涨落的维度依赖性。嵌有探针粒子的动力学受限东模型被用作超 Arrhenius 玻璃形成体系的代表。我们通过考虑通过有效分数 Stokes-Einstein 关系（D∼τ，其中 D 和 τ 分别是探针粒子的扩散常数和模型液体的弛豫时间，而 ω>0 则编码了标准 Stokes-Einstein 关系的破坏）来分离输运速率，来检验该模型中是否存在上临界维度。如果分离表明非平均场行为，则我们的模拟表明东模型在至少 d>10 以上具有上临界维度，并认为它实际上可能是无限的。这一结果是由于东模型在任何有限维度中都存在层次动力学。我们讨论了这些结果对于高维原子模型中分离研究的相关性。
