Articles in peer-reviewed journals
|Aperiodic extended surface perturbations in the Ising model|
|European Physical Journal B 11 (1999) 273|
|ArXiv : cond-mat/9811386 [PDF]|
|HAL : hal-00421975|
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 Îº of the distance l from the free surface with an oscillating amplitude Al = (-1)fl A where fl = 0, 1 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 Îº, the wandering exponent Ïo/oo which governs the fluctuation of the sequence and the bulk correlation length exponent Î½. Analytical results are obtained for the surface magnetization which displays a rich variety of critical behaviours in the (Îº, Ïo/oo)-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.