Critical behavior of an autocatalytic reaction model

Irreversible many-particle dynamical systems are relevant to a variety of phenomena in physics, chemistry, and biology. We present a study of an irreversible kinetic reaction model for a one-component autocatalytic reaction A+A→${\mathit{A}}_2$. In this model, if an atom adsorbing on a lattice site has any neighbors, it reacts with one of them with a probability 1-p, and the two atoms leave the lattice; otherwise the atom occupies the site. As p is varied, this model undergoes a second-order kinetic phase transition from a chemically reactive state with a partial occupation of the lattice to a completely covered state that corresponds to the ‘‘poisoning’’ phenomenon seen on catalysts. The transition is studied both analytically through various mean-field approximations and numerically in one, two, and three dimensions. Finite-size-scaling analysis of the critical behavior is used to find the static and dynamic critical exponents. These exponents are found to be consistent with the critical exponents in the Reggeon-field-theory directed-percolation universality class.