We analyze two alternative methods for determining the exponent $z$ of the contact process (CP) and Domany-Kinzel (DK) cellular automaton in Monte Carlo Simulations. One method employs mixed initial conditions, as proposed for magnetic models [Phys. Lett. A. \textbf{ 298}, 325 (2002)]; the other is based on the growth of the moment ratio $m(t)=< \rho ^{ 2}(t)> /< \rho (t)> ^{ 2}$ starting with all sites occupied. The methods provide reliable estimates for $z$ using the short time dynamics of the process. Estimates of $\nu_{ ||}$ are obtained using a method suggested by Grassberger.
Categories: cond-mat.stat-mech