  The random-field Ising model (RFIM) is one of the simplest
statistical-mechanical models that captures the anomalous irreversible
collective response seen in a wide range of physical, biological, or
socio-economic situations in the presence of interactions and intrinsic
heterogeneity or disorder. When slowly driven at zero temperature it can
display an out-of-equilibrium phase transition associated with critical scaling
("crackling noise"), while it undergoes at equilibrium, under either
temperature or disorder-strength changes, a thermodynamic phase transition. We
show that the out-of-equilibrium and equilibrium critical behaviors are in the
same universality class: they are controlled, in the renormalization-group (RG)
sense, by the same zero-temperature fixed point. We do so by combining a
field-theoretical formalism that accounts for the multiple metastable states
and the exact (functional) RG. As a spin-off, we also demonstrate that critical
fluids in disordered porous media are in the same universality class as the
RFIM, thereby unifying a broad spectrum of equilibrium and out-of-equilibrium
phenomena.
