Planar graph model of energy landscapes

Energy landscape models of glasses generally assume that unusual energy distributions are required for slow, glassy dynamics, for example ``trap'' models with infinitely deep holes. Here, we model energy landscapes with planar graphs where vertices represent configurations and edges represent possible transitions. The vertices are embedded in a two-dimensional plane and assigned energies. The edges are drawn such that only nearby vertices are accessible from any given vertex. In this case, we find two phases: a ``glassy'' one with sub-exponential relaxation and ``normal'' one with slightly super-exponential relaxation.