Absorbing phase transition in contact process on fractal lattices

We investigate the critical behavior of nonequilibrium phase transition from an active phase to an absorbing state on two selected fractal lattices, i.e., on a checkerboard fractal and on a Sierpinski carpet. The checkerboard fractal is finitely ramified with many dead ends, while the Sierpinski carpet is infinitely ramified. We measure various critical exponents of the contact process with a diffusion-reaction scheme A -> AA and A -> 0, characterized by a spreading with a rate lambda and an annihilation with a rate mu, and the results are confirmed by a crossover scaling and a finite-size scaling. The exponents, compared with the E-expansion results assuming is an element of = 4 - d(F),d(F) being the fractal dimension of the underlying fractal lattice, exhibit significant deviations from the analytical results for both the checkerboard fractal and the Sierpinski carpet. On the other hand, the exponents on a checkerboard fractal agree well with the interpolated results of the regular lattice for the fractional dimensionality, while those on a Sierpinski carpet show marked deviations. (c) 2007 Elsevier B.V. All rights reserved.