Searching for the Jamming Transition in the Energy Landscape Using a Transect Method*

The energy landscape associated with sphere packings is expected to host an astronomical number of local minima.  Arguments based on the Edwards ensemble suggest that this landscape should hold signatures of the jamming transition, at which point the number of minima are expected to diverge, and the distribution of volumes of each minima is expected to sharpen to a delta function.  However, it is impossible to exhaustively measure the entire landscape.  Instead, we employ the “transect method” [1], whereby we determine the local minima for every point along a random line drawn through the energy landscape.  Past work suggests that the number of minima encountered should scale linearly with the distance along the line subject to a logarithmic correction whose magnitude diverges at a phase transition.  This method has the potential to open a new window on the jamming transition seen as a phase transition across the entire energy landscape as opposed to a phase transition for each individual local minima.

[1] I. A. Kovács, F. Iglói and J. Cardy (2012) Corner contribution to percolation cluster numbers, Phys. Rev. B 86, 214203