### Abstract

We investigated the phase transition behavior of a binary spreading process in two dimensions for different particle diffusion strengths (D), We found that N>2 cluster mean-field approximations must be considered to get consistent singular behavior. The D=3,4 approximations result in a continuous phase transition belonging to a single universality class along the D ∈ (0,1) phase transition line. Large scale simulations of the particle density confirmed mean-field scaling behavior with logarithmic corrections. This is interpreted as numerical evidence supporting the bosonic field theoretical prediction that the upper critical dimension in this model is d_{c}=2. The pair density scales in a similar way but with an additional logarithmic factor to the order parameter. At the D = 0 end point of the transition line we found directed percolation criticality.

Original language | English |
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Article number | 056113 |

Pages (from-to) | 056113/1-056113/7 |

Journal | Physical Review E - Statistical, Nonlinear, and Soft Matter Physics |

Volume | 65 |

Issue number | 5 |

DOIs | |

Publication status | Published - May 1 2002 |

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics

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## Cite this

*Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*,

*65*(5), 056113/1-056113/7. [056113]. https://doi.org/10.1103/PhysRevE.65.056113