Volume 111, Number 4, August 2015
|Number of page(s)
|07 September 2015
One-dimensional Kac model of dense amorphous hard spheres
1 Department of Physics, Nagoya University - Nagoya, 464-8602, Japan
2 Fukui Institute for Fundamental Chemistry, Kyoto University - Takano-Nishihiraki-cho 34-4, Sakyo-ku, Kyoto, 606-8103, Japan
Received: 25 June 2015
Accepted: 8 August 2015
We introduce a new model of hard spheres under confinement for the study of the glass and jamming transitions. The model is a one-dimensional chain of the d-dimensional boxes each of which contains the same number of hard spheres, and the particles in the boxes of the ends of the chain are quenched at their equilibrium positions. We focus on the infinite-dimensional limit of the model and analytically compute the glass transition densities using the replica liquid theory. From the chain length dependence of the transition densities, we extract the characteristic length scales at the glass transition. The divergence of the lengths are characterized by the two exponents, for the dynamical transition and −1 for the ideal glass transition, which are consistent with those of the p-spin mean-field spin glass model. We also show that the model is useful for the study of the growing length scale at the jamming transition.
PACS: 05.20.-y – Classical statistical mechanics / 64.70.Q- – Theory and modeling of the glass transition / 83.80.Fg – Granular solids
© EPLA, 2015
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.