摘要翻译：
我们研究了玻璃态跃迁的动力学约束模型，并确定了哪些模型特征对于允许严格证明这些模型具有比幂律发散长度和时间尺度更快的不连续跃迁至关重要。我们研究的模型具有类似于由Toninelli，Biroli和Fisher(TBF)引入的knights模型的约束，但不同的邻居关系。我们发现，这种类似骑士的模型，也称为干扰渗流模型，需要一个“没有平行交叉”的规则，才能使玻璃跃迁的TBF证明有效。此外，大多数骑士类模型都不符合“没有垂直交叉”的要求，因此需要修改以使其更加严格。我们还通过观察比knights模型方向更稳定的模型，说明了“无平行交叉”要求如何用于评价其他相关渗流模型的可证明玻璃度。最后，我们证明了TBF证明不能以任何直截了当的方式推广到骑士模型的三维版本。
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英文标题：
《On the study of jamming percolation》
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作者：
M. Jeng, J. M. Schwarz
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最新提交年份：
2007
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分类信息：

一级分类：Physics        物理学
二级分类：Disordered Systems and Neural Networks        无序系统与神经网络
分类描述：Glasses and spin glasses; properties of random, aperiodic and quasiperiodic systems; transport in disordered media; localization; phenomena mediated by defects and disorder; neural networks
眼镜和旋转眼镜；随机、非周期和准周期系统的性质；无序介质中的传输；本地化；由缺陷和无序介导的现象；神经网络
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一级分类：Physics        物理学
二级分类：Statistical Mechanics        统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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英文摘要：
  We investigate kinetically constrained models of glassy transitions, and determine which model characteristics are crucial in allowing a rigorous proof that such models have discontinuous transitions with faster than power law diverging length and time scales. The models we investigate have constraints similar to that of the knights model, introduced by Toninelli, Biroli, and Fisher (TBF), but differing neighbor relations. We find that such knights-like models, otherwise known as models of jamming percolation, need a ``No Parallel Crossing'' rule for the TBF proof of a glassy transition to be valid. Furthermore, most knight-like models fail a ``No Perpendicular Crossing'' requirement, and thus need modification to be made rigorous. We also show how the ``No Parallel Crossing'' requirement can be used to evaluate the provable glassiness of other correlated percolation models, by looking at models with more stable directions than the knights model. Finally, we show that the TBF proof does not generalize in any straightforward fashion for three-dimensional versions of the knights-like models.
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PDF链接：
https://arxiv.org/pdf/708.0582