Jamming in a model glass: interplay of dynamics and thermodynamics

The relationship between extended structures, glassy dynamics and the presence of an underlying thermodynamic transition is explored in the context of lattice models of loops. We review the physical picture which emerges from numerical studies of loop models. It shows dynamical barriers and critical fluctuations combining to produce exponentially slow relaxations close to the critical point. The picture is further sharpened by comparing two loop models with equal dynamical barriers but different equilibrium fluctuations.