Relation between the two-dimensional self-avoiding walk and the Eden model

When the interface of a two-dimensional lattice gas is grown by an algorithm producing self-avoiding walks, some features of the Eden model appear. The scaling behavior of the widths and lengths of these interfaces and of their accessible perimeters are examined in several regions of the phase diagram. It is found that both the accessible perimeter and the interface behave like the Eden model below a critical point. Above this point, only the accessible perimeter behaves like the Eden model. The behavior in the critical region is suprisingly the same for the interface and its external perimeter but is different from the Eden model.