Aperiodic extended surface perturbations in the Ising model

L. Turban ()

The European Physical Journal B: Condensed Matter and Complex Systems, 1999, vol. 11, issue 2, 273-285

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 $A_l =( - 1)^{f_l } A$ where f l =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 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 (κ, ω)-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. Copyright Società Italiana di Fisica, Springer-Verlag 1999

Keywords: PACS. 05.50.+q Lattice theory and statistics (Ising; Potts; etc.); 68.35.Rh Phase transitions and critical phenomena (search for similar items in EconPapers)
Date: 1999
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DOI: 10.1007/BF03219169

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