RADIAL FREDHOLM PERTURBATION IN THE 2-DIMENSIONAL ISING-MODEL AND GAP-EXPONENT RELATION

We consider concentric circular defects in the two-dimensional Ising m odel, which are distributed according to a generalized Fredholm sequen ce, i.e, at exponentially increasing radii. This type of aperiodicity does not change the bulk critical behaviour but introduces a marginal extended perturbation. The critical exponent of the local magnetizatio n is obtained through finite-size scaling, using a corner transfer mat rix approach in the extreme anisotropic limit. It varies continuously with the amplitude of the modulation and is closely related to the mag netic exponent of the radial Hilhorst-van Leeuwen model. Through a con formal mapping of the system onto a strip, the gap-exponent relation i s shown to remain valid for such an aperiodic defect.