Random closest packing in a 2D lattice model

The dynamics of compaction of hard cross-shaped pentamers on the 2D square lattice is investigated. The addition of new particles is controlled by diffusive relaxation. It is shown that the filling process terminates at a glassy phase with a limiting coverage density rcp = 0.171 626(3), lower than the density of closest packing cp = (1/5), and the long-time filling rate vanishes like ( rcp - (t ))2 . For the entire density regime the particles form an amorphous phase, devoid of any crystalline order. Therefore, the model supports a stable random packing state, as opposed to the hard-discs system.