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

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

1999-06-09

arxiv.org/abs/cond-mat/9906133v1

Physics

Condensed Matter

Statistical Mechanics

9 pages (REVTEX), 2 figures (EPS), Phys. Rev. E (accepted)

Scientific paper

10.1103/PhysRevE.60.3396

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).

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