  We use computer simulations to investigate the extended phase diagram of a
supercooled liquid linearly coupled to a quenched reference configuration. An
extensive finite-size scaling analysis demonstrates the existence of a
random-field Ising model (RFIM) critical point and of a first-order transition
line, in agreement with recent field-theoretical approaches. The dynamics in
the vicinity of this critical point resembles the peculiar activated scaling of
RFIM-like systems, and the overlap autocorrelation displays a logarithmic
stretching. Our study demonstrates RFIM criticality in the thermodynamic limit
for a three-dimensional supercooled liquids at equilibrium.
