Scaling properties of the surface of the Eden model in d=2, 3, 4
Résumé
The surface of the Eden model is investigated numerically by finite-size scaling, using a strip geometry. Three different versions are studied and it shows that the one mostly used previously exhibits strong finite-size corrections. In two dimensions it is found that the surface thickness simply grows as the square root of the width of the strip for infinitely long strips. This result, as well as the results in d=3 and d=4, suggest that the surface of the Eden shares some properties with the equilibrium models used to describe the roughening transition. Moreover, it is found that the surface thickness scales differently with the height of the cluster for infinitely large strips.