  Using computer simulations of an atomistic glass-forming liquid, we
investigate the fluctuations of the overlap between a fluid configuration and a
quenched reference system. We find that large fluctuations of the overlap
develop as temperature decreases, consistent with the existence of the random
critical point that is predicted by effective field theories. We discuss the
scaling of fluctuations near the presumed critical point, comparing the
observed behaviour with that of the random-field Ising model. We argue that
this critical point directly reveals the existence of an interfacial tension
between amorphous metastable states, a quantity relevant both for equilibrium
relaxation and for nonequilibrium melting of stable glass configurations.
