Cluster Approximation for the Contact Process

TL;DR

This paper uses a cluster approximation to analyze the one-dimensional contact process, providing improved steady state descriptions and more accurate critical exponents than mean-field theory, despite limitations in critical behavior modeling.

Contribution

Introduces a cluster approximation method that better captures steady state properties and critical exponents of the contact process compared to traditional mean-field approaches.

Findings

Accurately describes steady state properties for various desorption rates.

Produces critical exponents closer to simulation results than mean-field theory.

Identifies limitations in modeling the critical behavior with the approximation.

Abstract

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.