Lack of universality in 2-dimensional multicomponent spreading phenomena

Magnetic entities are introduced in a two-dimensional Eden model as additional degrees of freedom in order to model multidomain spreading phenomena. The elements of the growth are "spins" taking q states and are coupled or not via an energy J, as in the Potts model, thus leading to a competition between species. The internal cluster spreading is found to result from a competition between growing domains. Complex mechanisms such as trapping, jamming and coalescence occur between the growing domains. A large variety of critical and nanuniversal regimes, from subcritical to self-organized critical behaviors, are obtained depending on nonuniversal parameters such as the lattice structure, the number of internal degrees of freedom q, and the coupling J. For the square lattice, the fractal dimension is 1.50 and the mass distribution exponent tau is 1.63. For the triangular lattice, the fractal dimension varies from 1.70 to 1.83 depending on the coupling value and the mass distribution exponent tau also varies from 1.67 to 1.98 depending on the coupling value. The correspondence and differences with respect to the percolation phenomenon are outlined.