Cluster Approximation for theContact Process,
E. Ben-Naim and P. L. Krapivsky
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.
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