  Facilitated spin models on random graphs provide an ideal microscopic
realization of the mode-coupling theory of supercooled liquids: they undergo a
purely dynamic glass transition with no thermodynamic singularity. In this
paper we study the fluctuations of dynamical heterogeneity and their
finite-size scaling properties in the beta relaxation regime of such
microscopic spin models. We compare the critical fluctuations behavior for two
distinct measures of correlations with the results of a recently proposed field
theoretical description based on quasi-equilibrium ideas. We find that the
theoretical predictions perfectly fit the numerical simulation data once the
relevant order parameter is identified with the persistence function of the
spins.
