Clusters and Frustration in Glass Forming Systems and Granular Materials

概要

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The static and dynamic properties of the frustrated percolation model are investigated. This model, which contains frustration as an essential ingredient, displays glassy behavior at high density or low temperature and in the extreme case of quenched disorder exhibits two transitions: a percolation transition at a temperature Tp with critical exponents of the ferromagnetic s = 1/2 state Potts model, and a second transition at a lower temperature To in the same universality class of the Ising spin glass model. Numerically it is found that Tp marks the onset of long time stretched exponential decay, while To coincides with the temperature where the diffusion coefficient vanishes. The model suggests for glass forming liquids a percolation temperature, above the glass transition To, where frustration effects start to be manifested. This transition gives rise to highly correlated localized clusters, which may be responsible of various precursor phenomena, such as onset of stretched exponentials, breakdown of Stokes Einstein relation, presence of dynamical heterogeneity. The model also suggests the existence of a diverging cooperative length which is manifested in large fluctuations of internal degrees of freedom, while density fluctuations behave smoothly through the transition. The model is also applied to describe the complex behavior of granular materials.
理論物理学刊行会の論文
1997-06-27