  We study a three-dimensional plaquette spin model whose low temperature
dynamics is glassy, due to localised defects and effective kinetic constraints.
While the thermodynamics of this system is smooth at all temperatures, we show
that coupling it to a second system with a fixed (quenched) configuration can
lead to a phase transition, at finite coupling. The order parameter is the
overlap between the copies, and the transition is between phases of low and
high overlap. We find critical points whose properties are consistent with
random-field Ising universality. We analyse the interfacial free energy cost
between the high- and low-overlap states that coexist at (and below) the
critical point, and we use this cost as the basis for a finite-size scaling
analysis. We discuss these results in the context of mean-field and dynamical
facilitation theories of the glass transition.
