Spiral model, jamming percolation and glass-jamming transitions

The Spiral Model (SM) corresponds to a new class of kinetically constrained models introduced in joint works with Fisher [9,10] which provide the first example of finite dimensional models with an ideal glass-jamming transition. This is due to an underlying jamming percolation transition which 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, leading to a Vogel-Fulcher-like divergence of the relaxation time. Here we present a detailed physical analysis of SM, see [6] for rigorous proofs.