### 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 |
---|---|

Article number | 056113 |

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

Volume | 65 |

Issue number | 5 |

DOIs | |

Publication status | Published - May 2002 |

### Fingerprint

### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Condensed Matter Physics
- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

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

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

**Phase transition of a two-dimensional binary spreading model.** / Ódor, G.; Marques, M. C.; Santos, M. A.

Research output: Contribution to journal › Article

*Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*, vol. 65, no. 5, 056113. https://doi.org/10.1103/PhysRevE.65.056113

}

TY - JOUR

T1 - Phase transition of a two-dimensional binary spreading model

AU - Ódor, G.

AU - Marques, M. C.

AU - Santos, M. A.

PY - 2002/5

Y1 - 2002/5

N2 - 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 dc=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.

AB - 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 dc=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.

UR - http://www.scopus.com/inward/record.url?scp=41349102535&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=41349102535&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.65.056113

DO - 10.1103/PhysRevE.65.056113

M3 - Article

VL - 65

JO - Physical review. E

JF - Physical review. E

SN - 2470-0045

IS - 5

M1 - 056113

ER -