MARGINAL ANISOTROPY IN LAYERED APERIODIC ISING SYSTEMS

Two-dimensional layered aperiodic Ising systems are studied in the ext reme anisotropic limit where they correspond to quantum Ising chains i n a transverse field. The modulation of the couplings follows an aperi odic sequence generated through substitution. According to Luck's crit erion, such a perturbation becomes marginal when the wandering exponen t of the sequence vanishes. Three marginal sequences are considered: t he period-doubling, paper-folding and three-folding sequences; They co rrespond to bulk perturbations for which the critical temperature is s hifted. The surface magnetization is obtained exactly for the three se quences. The scaling dimensions of the local magnetization on both sur faces, x(ms) and (x) over bar(ms), vary continuously with the modulati on factor. The low-energy excitations of the quantum chains are found to scale as L(z) with the size L of the system. This is the behaviour expected for a strongly anisotropic system, where z is the ratio of th e exponents of the correlation lengths in the two directions. The anis otropy exponent z is here simply equal to x(ms) + (x) over bar(ms). Th e anisotropic scaling behaviour is verified numerically for other surf ace and bulk critical properties as well.