Phase transition of a two dimensional binary spreading model

Details Phase transition of a two dimensional binary spreading model Phase transition of a two dimensional binary spreading model

2002-01-14

arxiv.org/abs/cond-mat/0201208v2

Physics

Condensed Matter

Statistical Mechanics

8 pages, 10 figures

Scientific paper

10.1103/PhysRevE.65.056113

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 $N=3,4$ approximations result in a continuous phase transition belonging to a single universality class along the $D\in (0,1)$ 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 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 endpoint of the transition line we found DP criticality.

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