CRITICAL-BEHAVIOR OF HIERARCHICAL ISING-MODELS

We consider the critical behavior of two-dimensional layered Ising mod els where the exchange couplings between neighboring layers follow hie rarchical sequences. The perturbation caused by the nonperiodicity cou ld be irrelevant, relevant, or marginal. For marginal sequences we hav e 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 ve rsion of the model. The critical exponents are found to vary continuou sly with the strength of the modulation, while close to the critical p oint the system is essentially anisotropic: the correlation length is diverging with different exponents along and perpendicular to the laye rs.