  We consider the critical behavior of two-dimensional layered Ising models
where the exchange couplings between neighboring layers follow hierarchical
sequences. The perturbation caused by the non-periodicity could be irrelevant,
relevant or marginal. For marginal sequences we have performed a detailed
study, which involved analytical and numerical calculations of different
surface and bulk critical quantities in the two-dimensional classical as well
as in the one-dimensional quantum version of the model. The critical exponents
are found to vary continuously with the strength of the modulation, while close
to the critical point the system is essentially anisotropic: the correlation
length is diverging with different exponents along and perpendicular to the
layers.
