  We consider the surface critical behaviour of a semi-infinite two-dimensional
layered Ising model, where the couplings perpendicular to the surface follow
the aperiodic Rudin-Shapiro sequence. The model has unusual critical
properties: depending on the strength of the modulation, at the bulk critical
point the surface magnetization is either discontinuous or vanishes with an
essential singularity. The critical surface magnetization as well as the form
of the essential singularity are calculated exactly.
