EXACT RENORMALIZATION-GROUP STUDY OF APERIODIC ISING QUANTUM CHAINS AND DIRECTED WALKS

We consider the Ising model and the directed walk on two-dimensional l ayered lattices and show that the two problems are inherently related: The zero-field thermodynamical properties of the Ising model are cont ained in the spectrum of the transfer matrix of the directed walk. The critical properties of the two models are connected to the scaling be havior of the eigenvalue spectrum of the transfer matrix which is stud ied exactly through renormalization for different self-similar distrib utions of the couplings. The models show very rich bulk and surface cr itical behaviors with nonuniversal critical exponents, coupling-depend ent anisotropic scaling, first-order surface transition, and stretched exponential critical correlations. It is shown that all the nonuniver sal critical exponents obtained for the aperiodic Ising models satisfy scaling relations and can be expressed as functions of varying surfac e magnetic exponents. [S0163-1829(97)00441-4].