Journal of Physics A Mathematical and General

Critical behaviour in aperiodic systems

Ferenc Iglói

Published Aug 7, 1993• 77 citations

Abstract

The author considers layered systems with aperiodically modulated couplings and study the effect of inhomogeneity on the critical behaviour. Using scaling arguments a relevance/irrelevance-type criterion is formulated and for relevant inhomogeneities the scaling form of singular quantities is determined. The author has performed exact calculations for the surface magnetization of aperiodic quantum Ising chains and for a (1+1)-dimensional directed polymer in a longitudinal aperiodic environment. The results for both systems are in accord with scaling considerations. For a marginal aperiodicity the critical exponents are found to be non-universal.

DOI: 10.1088/0305-4470/26/15/016

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Journal of Physics A Mathematical and General

Critical behaviour in aperiodic systems

Ferenc Iglói

Published Aug 7, 1993• 77 citations

Publisher

Abstract

DOI: 10.1088/0305-4470/26/15/016

Related papers

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Pierre Emmanuel Berche, Bertrand Berche, Loïc Turban

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arXiv:cond-mat/9811386The European Physical Journal BJan 1, 19992 citations

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.