Radial Fredholm perturbation in the two-dimensional Ising model and gap-exponent relation

Dragi Karevski (1) , Loic Turban (1) , Ferenc Iglói (2)

1 IJL - Institut Jean Lamour
2 Research Institute for Solid State Physics and Optics [Budapest]

We consider concentric circular defects in the two-dimensional Ising model, which are distributed according to a generalized Fredholm sequence, 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 magnetization is obtained through finite-size scaling, using a corner transfer matrix approach in the extreme anisotropic limit. It varies continuously with the amplitude of the modulation and is closely related to the magnetic exponent of the radial Hilhorst-van Leeuwen model. Through a conformal mapping of the system onto a strip, the gap-exponent relation is shown to remain valid for such an aperiodic defect.

Domaines: Autre [cond-mat.other]

Dragi Karevski, Loic Turban, Ferenc Iglói. Radial Fredholm perturbation in the two-dimensional Ising model and gap-exponent relation. Journal of Physics A General Physics (1968-1972), 1995, 28, pp.3925. ⟨10.1088/0305-4470/28/14/013⟩. ⟨hal-00421995⟩