Oscillatory behavior of critical amplitudes of the Gaussian model on a hierarchical structure

We studied oscillatory behavior of critical amplitudes for the Gaussian mod el on a hierarchical structure presented by a modified Sierpinski gasket la ttice. This model is known to display nonstandard critical behavior on the lattice under study. The leading singular behavior of the correlation lengt h xi near the critical coupling K=K-c is modulated by a function which is p eriodic in ln\ln(K-c-K)\. We have also shown that the common finite-size sc aling 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 beh avior of xi differs from the one described earlier (which was based on the finite-size scaling assumption). [S1063-651X(99)05609-3].