Groupe de Physique Statistique/ Arbeitsgruppe Statistische Physik

We investigate the surface critical behavior of two-dimensional multilayered aperiodic Ising models in the extreme anisotropic limit. The system under consideration is obtained by piling up two types of layers with, respectively, p and q spin rows coupled via nearest-neighbor interactions λr and λ, where the succession of layers follows an aperiodic sequence generated through substitution rules. Far away from the critical regime, the correlation length ΟâS¥, measured in lattice spacing units, in the direction perpendicular to the layers is smaller than the first-layer width and the system exhibits the usual behavior of an ordinary surface transition. In the other limit, in the neighborhood of the critical point, ΟâS¥ diverges and the fluctuations are sensitive to the nonperiodic structure of the system so that the critical behavior is governed by another fixed point. We determine the critical exponent associated to the surface magnetization at the aperiodic critical point and show that the expected crossover between the two regimes is well described by a scaling function. From numerical calculations, the parallel correlation length Οâ^¥ is then found to behave with an anisotropy exponent ; which depends on the aperiodic modulation and the layer widths.