MAGNETIC CRITICAL-BEHAVIOR OF THE ISING-MODEL ON FRACTAL STRUCTURES

The critical temperature and the set of critical exponents (beta, gamm a, nu) of the Ising model on a fractal structure, namely the Sierpinsk i carpet, are calculated from a Monte Carlo simulation based on the Wo lff algorithm together with the histogram method and finite-size scali ng. Both cases of periodic boundary conditions and free edges are inve stigated. The calculations have been done up to the seventh iteration step of the fractal structure. The results show that, although the str ucture is not translationally invariant, the scaling behavior of therm odynamical quantities is conserved, which gives a meaning to the finit e-size analysis. Although some discrepancies in the values of the crit ical exponents occur between periodic boundary conditions and free edg es, the effective dimension obtained through the Rushbrooke and Joseph son's scaling law have the same value in both cases. This value is sli ghtly but significantly different from the fractal dimension.