We refute in this Reply the criticisms made by M. Abdel-Aty [Phys. Rev. A 70, 047801 (2004)]. We show that none of them are founded and we demonstrate very explicitly what is wrong in the arguments developed by this author.
We reply to the Comment by Aryanpour, Maier, and Jarrell [Phys. Rev. B 71, 037101 (2005)] on our paper [Phys. Rev. B 65, 155112 (2002)]. We demonstrate, using general arguments and explicit examples, that whenever the correlation length is finite, local observables converge exponentially fast in the cluster size Lc within cellular dynamical mean field theory. This is a faster rate of convergence than the 1∕Lc2 behavior of the dynamical cluster approximation, thus refuting the central assertion of their Comment.