  Criticality in the class of disordered systems comprising the random-field
Ising model (RFIM) and elastic manifolds in a random environment is controlled
by zero-temperature fixed points that must be treated through a functional
renormalization group. We apply the nonperturbative functional renormalization
group approach that we have previously used to describe the RFIM in and out of
equilibrium [Balog-Tarjus-Tissier, Phys. Rev. B 97, 094204 (2018)] to the
simpler and by now well-studied case of the random elastic manifold model. We
recover the main known properties, critical exponents and scaling functions, of
both the pinned phase of the manifold at equilibrium and the depinning
threshold in the athermally and quasi-statically driven case for any dimension
$0<d\leq 4$. This successful benchmarking of our theoretical approach gives
strong support to the results that we have previously obtained for the RFIM, in
particular concerning the distinct universality classes of the equilibrium and
out-of-equilibrium (hysteresis) critical points below a critical dimension
$d_{DR}\approx 5.1$.
