Hysteresis scaling for Ising systems on fractal structures

Dynamical phase transitions in Ising systems on Sierpinski Carpets and bond-percolation lattices at percolation threshold are studied by means of standard Monte Carlo simulations. We find that the area of hysteresis loop A can be scaled with respect to the sweep rate h of a linear driving field. However, the exponent in the scaling expression, A hb, is universal only for Ising systems on Sierpinski carpets. We conclude that the hysteresis scaling is universal for the field-driven first-order phase transitions in Ising systems on fractal structures. Based on scaling hypothesis, we derive the expression of finite-size effect on the hysteresis. The exponent b is obtained by this method in some Sierpinski carpets.