Eur. Phys. J. B 11, 273-285 (1999)
https://doi.org/10.1007/s100510050938

Aperiodic extended surface perturbations in the Ising model

Laboratoire de Physique des Matériaux (CNRS UMR 7556) , Université Henri Poincaré, BP 239, 54506 Vandœuvre lès Nancy Cedex, France

Corresponding author: ^a turban@lps.u-nancy.fr

Received: 1 December 1998
Published online: 15 September 1999

Abstract

We study the influence of an aperiodic extended surface perturbation on the surface critical behaviour of the two-dimensional Ising model in the extreme anisotropic limit. The perturbation decays as a power κ of the distance l from the free surface with an oscillating amplitude where follows some aperiodic sequence with an asymptotic density equal to 1/2 so that the mean amplitude vanishes. The relevance of the perturbation is discussed by combining scaling arguments of Cordery and Burkhardt for the Hilhorst-van Leeuwen model and Luck for aperiodic perturbations. The relevance-irrelevance criterion involves the decay exponent κ, the wandering exponent ω which governs the fluctuation of the sequence and the bulk correlation length exponent ν. Analytical results are obtained for the surface magnetization which displays a rich variety of critical behaviours in the -plane. The results are checked through a numerical finite-size-scaling study. They show that second-order effects must be taken into account in the discussion of the relevance-irrelevance criterion. The scaling behaviours of the first gap and the surface energy are also discussed.