M. Knezevic et D. Knezevic, Oscillatory behavior of critical amplitudes of the Gaussian model on a hierarchical structure, PHYS REV E, 60(3), 1999, pp. 3396-3398
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].