Phase transition of a two-dimensional binary spreading model

We investigated the phase transition behavior of a binary spreading process in two dimensions for different particle diffusion strengths $\mathrm{}\left(D\right).$ We found that $N>\mathrm{}2\mathrm{}$ cluster mean-field approximations must be considered to get consistent singular behavior. The $N=3,4\mathrm{}$ approximations result in a continuous phase transition belonging to a single universality class along the $D\in \mathrm{}(0,1)\mathrm{}$ 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 $d_c=2.\mathrm{}$ The pair density scales in a similar way but with an additional logarithmic factor to the order parameter. At the $D=0\mathrm{}$ end point of the transition line we found directed percolation criticality.