SURFACE MAGNETIZATION AND CRITICAL-BEHAVIOR OF APERIODIC ISING QUANTUM CHAINS

We consider semi-infinite two-dimensional layered Ising models in the extreme anisotropic limit with an aperiodic modulation of the coupling s. Using substitution rules to generate the aperiodic sequences, we de rive functional equations for the surface magnetization. These equatio ns are solved by iteration and the critical exponent beta(s) can be de termined exactly. The method is applied to three specific aperiodic se quences, which represent different types of perturbation, according to a relevance-irrelevance criterion. On the Thue-Morse lattice, for whi ch the modulation is an irrelevant perturbation, the surface magnetiza tion vanishes with a square-root singularity, like in the homogeneous lattice. For the period-doubling sequence, the perturbation is margina l and beta(s) is a continuous function of the modulation amplitude. Fi nally, the Rudin-Shapiro sequence, which corresponds to the relevant c ase, displays an anomalous surface critical behavior which is analyzed via scaling considerations. Depending on the value of the modulation, the surface magnetization either vanishes with an essential singulari ty or remains finite at the bulk critical point, i.e., the surface pha se transition is of first order.