Absorbing phase transition in a parity-conserving particle process on a Sierpinski carpet fractal

Abstract

We study a stochastic lattice model with parity-conserving particle process using a Monte Carlo procedure. We perform simulations on a Sierpinski carpet fractal with dimension D f = ln 8/ ln 3. We calculate the critical exponents at the threshold of the absorbing phase transition at the known value for the critical diusion p c = 1 (Cardy and Tauber 1996 Phys. Rev. Lett. 77 4780). Using finite-size and finite-time scaling analysis we calculate the critical exponents at p c = 1 and below, where a finite density of particles is found in the long-time limit. From dynamic simulations we calculate the dynamical exponents Z, δ, ν , ν ⊥ and γ , /Zν ⊥ , and they are found to dier from the mean-field values, as well as the stationary exponent β. We check the consistence of the results with the hyperscaling relation.