Study of a monomer-monomer reaction system with short-range repulsive interactions

The critical behavior of an interacting two species catalytic surface reaction model is studied by means of Monte Carlo simulations and a mean-field approach. The model has two parameters, namely the relative adsorption rate of species p <Subscript> A </Subscript> and a short-range repulsive interaction r between the same type of adsorbed species. The system exhibits an stationary reactive phase and two symmetrically equivalent absorbing phases. These latter phases are unique and correspond to surfaces saturated by a single type of reacting species. For <InlineEquation ID="Equ1"> <EquationSource Format="TEX">$r > 0 \wedge r \neq 1$</EquationSource> </InlineEquation>, the system exhibits a second-order phase transition that belongs to the directed percolation (DP) universality class. However, in the absence of repulsive interaction (r=0), a bicritical point is found at p <Subscript> A </Subscript>=1/2 whose critical behavior is compatible with dynamical mean-field exponents. Our findings indicate that the bicritical point belongs to the Voter Model universality class, whose upper critical dimension is d <Subscript> c </Subscript>=2. In addition, we propose a method to study the crossover from MF to DP behavior based on the estimation of the crossover time T <Subscript> c </Subscript>. We find that T <Subscript> c </Subscript> diverges according to a power-law <InlineEquation ID="Equ2"> <EquationSource Format="TEX">$T_{c} \propto r^{-\mu}$</EquationSource> </InlineEquation> as <InlineEquation ID="Equ3"> <EquationSource Format="TEX">$r \rightarrow 0$</EquationSource> </InlineEquation> where <InlineEquation ID="Equ4"> <EquationSource Format="TEX">$\mu \simeq 1.17 \pm 0.03$</EquationSource> </InlineEquation> is the crossover exponent. For strong repulsion, a new transient effect appears associated with the onset of almost inactive “chessboad” patterns. Copyright Springer-Verlag Berlin/Heidelberg 2004