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 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).