Universal behaviour for a 1+1 growth model

In a recent work [1] a method to derive analytically the roughness evolution was exposed. The method allows to obtain analytically the growths exponents of a surface of $1+1$ dimensions whose dynamics is ruled by cellular automata. The method was successfully applied to the etching model [2,3] and the dynamical exponents where obtained. Those exponents are exact and they are the same as those exhibited by the KPZ model [4] for this dimension. We applied the method as well to RSOS model [5,6] and we confirm that the very old conjecture that, the RSOS model and KPZ belong to the same universality class. We show as well a very general procedure to classify the models without hard calculations. This method allows us to verify the universality class of the automata cellular model [7].\\

[1] W. S. Alves {\bf et al} to be published.

[2] B. A. Mello, A. S. Chaves, and F. A. Oliveira, Phys. Rev. E {\bf 63}, 041113 (2001).

[3] E. A. Rodrigues, B. A. Mello, and F. A. Oliveira, J. Phys. A {\bf 48}, 035001 (2015).

[4] M. Kardar, G. Parisi, and Y. C. Zhang, Phys. Rev. Lett. {\bf 56}, 9, 889 (1986).

[5] Halpin-Healy T J and Zhang C-Y, Phys. Rep. {\bf 254}, 215 (1995).

[6] Marsili M, Maritan A, Toigo F and Banavar J R, Rev. Mod. Phys. {\bf 68}, 963 (1996).

[7] W. R. Julvito {\bf et al} to be published.