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Jamming Percolation and Glassy Dynamics

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Abstract

We present a detailed physical analysis of the dynamical glass-jamming transition which occurs for the so called Knight models recently introduced and analyzed in a joint work with D.S. Fisher (Toninelli et al., Phys. Rev. Lett. 96, 035702, 2006). Furthermore, we review some of our previous works on Kinetically Constrained Models.

The Knight models correspond to a new class of kinetically constrained models which provide the first example of finite dimensional models with an ideal glass-jamming transition. This is due to the underlying percolation transition of particles which are mutually blocked by the constraints. This jamming percolation has unconventional features: it is discontinuous (i.e. the percolating cluster is compact at the transition) and the typical size of the clusters diverges faster than any power law when ρ ↗ ρ c . These properties give rise for Knight models to an ergodicity breaking transition at ρ c : at and above ρ c a finite fraction of the system is frozen. In turn, this finite jump in the density of frozen sites leads to a two step relaxation for dynamic correlations in the unjammed phase, analogous to that of glass forming liquids. Also, due to the faster than power law divergence of the dynamical correlation length, relaxation times diverge in a way similar to the Vogel-Fulcher law.

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Authors and Affiliations

  1. Institut des Hautes Études Scientifiques, Le Bois-Marie 35, Route de Chartres, F-91440, Bures-sur-Yvette, France

    Cristina Toninelli

  2. Service de Physique Théorique, CEA/Saclay-Orme des Merisiers, F-91191, Gif-sur-Yvette Cedex, France

    Giulio Biroli

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  1. Cristina Toninelli
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  2. Giulio Biroli
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Correspondence to Cristina Toninelli.

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Toninelli, C., Biroli, G. Jamming Percolation and Glassy Dynamics. J Stat Phys 126, 731–763 (2007). https://doi.org/10.1007/s10955-006-9177-9

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  • DOI: https://doi.org/10.1007/s10955-006-9177-9

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