Stationary and dynamic critical behavior of the contact process on the Sierpinski carpet

We investigate the critical behavior of a stochastic lattice model describing a contact process in the Sierpinski carpet with fractal dimension d=log8/log3. We determine the threshold of the absorbing phase transition related to the transition between a statistically stationary active and the absorbing states. Finite-size scaling analysis is used to calculate the order parameter, order parameter fluctuations, correlation length, and their critical exponents. We report that all static critical exponents interpolate between the line of the regular Euclidean lattices values and are consistent with the hyperscaling relation. However, a short-time dynamics scaling analysis shows that the dynamical critical exponent Z governing the size dependence of the critical relaxation time is found to be larger then the literature values in Euclidean d=1 and d=2, suggesting a slower critical relaxation in scale-free lattices.