Absorbing phase transition in conserved lattice gas model on fractal lattices

We study the continuous phase transition of the conserved lattice gas (CLG) model from an active phase into an absorbing phase on two fractal lattices, i.e., on a checkerboard fractal and on a Sierpinski gasket. In the CLG model, a particle is assumed to be active if any of the neighboring sites are occupied by a particle and inactive if all neighboring sites are empty. We estimate critical exponents theta, beta, nu||, and nu perpendicular, characterizing, respectively, the density of active particles in time, the order parameter, the temporal and spatial correlation lengths near the critical point, and the results are confirmed by off-critical scaling and finite size scaling. The order parameter exponent beta on a checkerboard fractal appears to lie between the one-dimensional (1D) value and two-dimensional (2D) value of the CLG model, while that on a Sierpinski gasket lies between the 1D and 2D values of the conserved threshold transfer process. Such a difference is manifested based on the intrinsic properties of the underlying fractal lattices.