Oscillatory Behavior of Critical Amplitudes of the Gaussian Model on a Hierarchical Structure

We studied oscillatory behavior of critical amplitudes for the Gaussian model on a hierarchical structure presented by a modified Sierpinski gasket lattice. This model is known to display non-standard critical behavior on the lattice under study. The leading singular behavior of the correlation leng...

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Bibliographic Details
Published in:arXiv.org 1999-06
Main Authors: Knezevic, Milan, Knezevic, Dragica
Format: Article
Language:English
Subjects:
Amplitudes
Scaling
Structural hierarchy
Online Access:Get full text
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Summary:We studied oscillatory behavior of critical amplitudes for the Gaussian model on a hierarchical structure presented by a modified Sierpinski gasket lattice. This model is known to display non-standard critical behavior on the lattice under study. The leading singular behavior of the correlation length \(\xi\) near the critical coupling \(K=K_c\) is modulated by a function which is periodic in \(\ln|\ln(K_c-K)|\). We have also shown that the common finite-size scaling hypothesis, according to which for a finite system at criticality \(\xi\) should be of the order of the size of system, is not applicable in this case. As a consequence of this, the exact form of the leading singular behavior of \(\xi\) differs from the one described earlier (which was based on the finite-size scaling assumption).
ISSN:2331-8422
DOI:10.48550/arxiv.9906133