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 nonstandard 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 the 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).