  Tensor networks representations of many-body quantum systems can be described
in terms of quantum channels. We focus on channels associated with the
Multi-scale Entanglement Renormalization Ansatz (MERA) tensor network that has
been recently introduced to efficiently describe critical systems. Our approach
allows us to compute the MERA correspondent to the thermodynamic limit of a
critical system introducing a transfer matrix formalism, and to relate the
system critical exponents to the convergence rates of the associated channels.
