  Recently, considerable progress has been made in understanding finite-size
scaling in equilibrium systems. Here, we study finite-size scaling in
non-equilibrium systems at the instance of directed percolation (DP), which has
become the paradigm of non-equilibrium phase transitions into absorbing states,
above, at and below the upper critical dimension. We investigate the
finite-size scaling behavior of DP analytically and numerically by considering
its steady state generated by a homogeneous constant external source on a
d-dimensional hypercube of finite edge length L with periodic boundary
conditions near the bulk critical point. In particular, we study the order
parameter and its higher moments using renormalized field theory. We derive
finite-size scaling forms of the moments in a one-loop calculation. Moreover,
we introduce and calculate a ratio of the order parameter moments that plays a
similar role in the analysis of finite size scaling in absorbing nonequilibrium
processes as the famous Binder cumulant in equilibrium systems and that, in
particular, provides a new signature of the DP universality class. To
complement our analytical work, we perform Monte Carlo simulations which
confirm our analytical results.
