Cluster Approximation for the Contact Process
  The one-dimensional contact process is analyzed by a cluster approximation. In this approach, the hierarchy of rate equations for the densities of finite length empty intervals are truncated under the assumption that adjacent intervals are not correlated. This assumption yields a first order phase transition from an active state to the adsorbing state. Despite the apparent failure of this approximation in describing the critical behavior, our approach provides an accurate description of the steady state properties for a significant range of desorption rates. Moreover, the resulting critical exponents are closer to the simulation values in comparison with site mean-field theory. 
E. Ben-Naim and P. L. Krapivsky