Comment on ``Jamming Percolation and Glass Transitions in Lattice Models.''

Abstract

Toninelli, Biroli, and Fisher recently introduced the knights model, a correlated percolation system (Phys. Rev. Lett. 96, 035702 (2006)). They claimed to prove that the critical point of this model was the same as that for directed percolation, and then used this to show (assuming a conjecture about directed percolation, described later in a more detailed proof) that this model has a discontinuous phase transition with a diverging correlation length. However, there is an error in their work, so that these results are unproven for their model. Their proofs can, however, be modified to work for a similar model.