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

TL;DR

This paper critiques a recent study on the knights model, highlighting an error in their proof of the phase transition's nature, and discusses how their methods could be adapted for a related model.

Contribution

It identifies an error in the previous proof regarding the knights model and suggests modifications for similar models to establish phase transition properties.

Findings

The original proof contains an unverified assumption.

The error affects conclusions about the phase transition.

Modified proofs could potentially establish similar results.

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.