  We study static and dynamic spatial correlations in a two-dimensional spin
model with four-body plaquette interactions and standard Glauber dynamics by
means of analytic arguments and Monte Carlo simulations. We study in detail the
dynamical behaviour which becomes glassy at low temperatures due to the
emergence of effective kinetic constraints in a dual representation where spins
are mapped to plaquette variables. We study the interplay between non-trivial
static correlations of the spins and the dynamic `four-point' correlations
usually studied in the context of supercooled liquids. We show that slow
dynamics is spatially heterogeneous due to the presence of diverging
lengthscales and scaling, as is also found in kinetically constrained models.
This analogy is illustrated by a comparative study of a froth model where the
kinetic constraints are imposed.
