Percolation and the Glass Transition - Kinetically-Constrained Models, Bootstrap Percolation, Mixed-Order Phase Transitions, and Large Deviations
Tel Aviv University, Israel
Please refer to the WORKSHOP WEBSITE for detailed and updated information.
There is currently much activity, both in the mathematics and in the physics communities, on kinetically-constrained models, bootstrap percolation, mixed-order phase transitions, and large deviations. In recent years, many connections between these four themes have emerged, thus contributing to the worldwide efforts to theoretically understand how the dynamics are halted in a wide variety of disordered many-body systems. An ordered crystalline phase is thermodynamically stable for atoms or molecules comprising a structural glass, for the spins in various metals and magnetic materials, for the colloids that give pastes their mechanical rigidity, for grains in a powder, and for particles in many other soft materials. Yet, when realistically prepared, they all jam in metastable disordered glassy states. The way that many-body systems become glassy as the density of the particles comprising them increases or their temperature decreases is still not fully understood.
The topics defining this workshop may be seen to be strongly linked, for example by the following recent finding: There is a strong relationship between the dynamics of some kinetically-constrained models and variants of bootstrap percolation; Mixed-order phase transitions appear in several contexts related to glassy systems. In particular, kinetically-constrained models, mean-field glassy systems and also bootstrap percolation display such unusual transitions on random graphs: the order parameter, e.g. fraction of blocked sites, has a discontinuous jump at the transition but it is also characterized by a critical behavior when approaching it; The study of large deviations, in particular in space-time, was shown to be a useful tool to characterize the slow dynamics displayed by kinetically-constrained models and by more general glassy systems.
The workshop will bring together leading statistical physicists and mathematicians working in these areas with the aim of highlighting recent results, fostering cross-interactions, establishing new connections and developing existing ones.
Giulio Biroli (CEA Saclay) - Organiser
Cristina Toninelli (University Paris 6-7) - Organiser
David Mukamel (Weizmann Institute of Science) - Organiser
Yair Shokef (Tel Aviv University) - Organiser