Critical behavior of the Ising model on fractal structures in dimensions between one and two: finite-size scaling effects - art. no. 184420

The magnetic critical behavior of Ising spins located at the sites of deter ministic Sierpinski carpets is studied within the framework of a ferromagne tic Ising model. A finite-size scaling analysis is performed from Monte Car lo simulations. We investigate four different fractal dimensions between 1. 9746 and 1.7227, up to the sixth and eighth iteration step of the fractal s tructure in one case. It turns out that the finite-size scaling behavior of most thermodynamical quantities is affected by scaling corrections increas ing as the fractal dimension decreases. tending towards the lower critical dimension of the Ising model. These corrections are related to the topology of the fractal structure and to the scale invariance. Nevertheless the max ima of the susceptibility follow power laws in a very reliable way. which a llows us to calculate the ratio of the exponents gamma /v. Moreover, the fi xed point of the fourth order cumulant at T-c exhibited by Binder on transl ation invariant lattices is replaced by a decreasing sequence of intersecti on points converging towards the critical temperature. The convergence towa rds the thermodynamical limit as the size of the networks increases is slow ed down as the fractal dimension decreases. At last, the evolution of the d iscrepancies between Monte Carte simulations and epsilon expansions with th e fractal dimension is set out.