Abstract
We provide an overall picture of the magnetic critical behavior of the Ising and three-state Potts models on tractal structures. The results brought out from Monte Carlo simulations for several Hausdorff dimensions between 1 and 3 show that this behavior can be understood in the framework of weak universality. Moreover, the maxima of the susceptibility follow power laws in a very reliable way, which allows us to calculate the ratio of the exponents γ/v and the anomalous dimension exponent η in a reliable way. At last, the evolution of these exponents with the Hausdorff dimension is discussed. © 2002 Elsevier Science B.V. All rights reserved.