Finite size scaling for directed percolation and related stochastic evolution processes

Finite size scaling effects are investigated for certain evolution processes modelled by a one-component reaction-diffusion system with an absorbing state. The model possesses a non-equilibrium critical point, and the associated universality class includes directed bond percolation, cellular automata, Reggeon field theory and a stochastic version of Schlögl's first autocatalytic reaction scheme. Using renormalisation group techniques, we calculate the linear relaxation time in a cubic geometry of finite sizeL, with periodic boundary conditions imposed. The corresponding scaling behaviour toO() (=4–d,d being the spatial dimension) is presented in universal form.