Zero-temperature criticality in a simple glass model

We introduce the strongly-interacting trap model, a version of Bouchaud's trap model for glasses [Bouchaud J-P 1992 {\em J. Phys. I France {\bf 2}} 1705]. At finite temperatures the model exhibits glassy relaxation over intermediate timeframes but reaches a steady state at finite times. In limit of zero temperature and with a suitably renormalised timescale the model maps onto the Bak-Sneppen model, widely studied in the context of self-organised criticality [Bak P and Sneppen K 1993 {\em Phys. Rev. Lett. {\bf 71}} 4083]. Hence zero temperature is a critical point in all dimensions. These claims are supported by mean field analysis of the stationary solution and numerical simulations of a finite-dimensional lattice model.