Surface Magnetisation and Surface Correlations in Aperiodic Ising Models

We consider the surface critical behaviour of diagonally layered Ising models on the square lattice where the inter-layer couplings follow some aperiodic sequence. The surface magnetisation is analytically evaluated from a simple formula derived by the diagonal transfer matrix method, while the surface spin-spin correlations are obtained numerically by a recursion method, based on the star-triangle transformation. The surface critical behaviour of different aperiodic Ising models are found in accordance with the corresponding relevance-irrelevance criterion. For marginal sequences the critical exponents are continuously varying with the strength of aperiodicity and generally the systems follow anisotropic scaling at the critical point.