  We numerically study the equilibrium relaxation dynamics of a two-dimensional
Mari-Kurchan glass model. The tree-like structure of particle interactions
forbids both non-trivial structural motifs and the emergence of a complex
free-energy landscape leading to a thermodynamic glass transition, while the
finite-dimensional nature of the model prevents the existence of a
mode-coupling singularity. Nevertheless, the equilibrium relaxation dynamics is
shown to be in excellent agreement with simulations performed in conventional
glass-formers. Averaged time-correlation functions display a phenomenology
typical of supercooled liquids, including the emergence of an excess signal in
relaxation spectra at intermediate frequencies. We show that this evolution is
accompanied by strong signatures of collective and heterogeneous dynamics which
cannot be interpreted in terms of single particle hopping and emerge from
dynamic facilitation. Our study demonstrates that an off-lattice interacting
particle model with extremely simple structural correlations displays
quantitatively realistic glassy dynamics.
