Two-component spreading phenomena: Why the geometry makes the criticality

We have numerically and theoretically investigated a simple model for two-component spreading phenomena in two different growth geometries (i.e., spreading confined in a half space and spreading in a free space). The criticality of the domain substructures unexpectedly depends on the considered geometry. This is understood by simple arguments of domain-wall particle diffusion and annihilation. We derive a relationship between the critical exponents chi and alpha for domain-wall spatial distributions in different geometries. The latter relationship is numerically verified in two, three and four dimensions.