Static and dynamical critical behavior of the monomer–monomer reaction model with desorption

• The monomer–monomer reaction model (A+B→AB)(A+B→AB) in the linear chain. The BB monomer desorbs with probability αα.
• The model displays a continuous phase transition from an absorbing phase into a reactive steady state.
• The critical behavior was studied by mean field theory (site and pair approximations) and Monte Carlo simulations.
• The model exhibits the same critical exponents of the directed universality class.

We studied in this work the monomer–monomer reaction model on a linear chain. The model is described by the following reaction: A+B→ABA+B→AB, where AA and BB are two monomers that arrive at the surface with probabilities yAyA and yByB, respectively, and we have considered desorption of the monomer BB with probability αα. The model is studied in the adsorption controlled limit where the reaction rate is infinitely larger than the adsorption rate. We employ site and pair mean-field approximations as well as static and dynamical Monte Carlo simulations. We show that the model exhibits a continuous phase transition between an active steady state and an A-absorbing state, when the parameter yAyA is varied through a critical value, which depends on the value of αα. Monte Carlo simulations and finite-size scaling analysis near the critical point are used to determine the static critical exponents ββ and ν⊥ν⊥ and the dynamical critical exponents ν∥ν∥ and zz. The results found for the monomer–monomer reaction model with BB desorption, in the linear chain, are different from those found by E. V. Albano (Albano, 1992) and are in accordance with the values obtained by Jun Zhuo and Sidney Redner (Zhuo and Redner, 1993), and endorse the conjecture of Grassberger, which states that any system undergoing a continuous phase transition from an active steady state to a single absorbing state, exhibits the same critical behavior of the directed percolation universality class.