Critical behaviour of the irreversible phase transitions of a dimer-monomer process on fractal media

Abstract

The dynamic critical behaviour of a dimer-monomer surface reaction process (the ZGB model) of the type 1/2 A2+B to AB is studied on two different fractals, namely a Sierpinski carpet and percolating clusters, which have almost the same fractal dimension DF equivalent to 1.89. In both surfaces, the model exhibits two continuous irreversible phase transitions. For the Sierpinski carpet the values of the critical exponents interpolate between those of directed percolation in 1+1 and 1+2 dimensions. Results corresponding to percolating clusters are not conclusive enough to assign the universality class of the model.