Competing reaction model with many absorbing configurations

Abstract

We study a competitive reaction model between two monomers A and B on a linear lattice. We assume that monomer A can react with a nearest-neighbor monomer A or B , but reactions between monomers of type B are prohibited. We include in our model lateral interactions between monomers as well as the effects of temperature of the catalyst. The model is considered in the adsorption controlled limit, where the reaction rate is infinitely larger than the adsorption rate of the monomers. We employ site and pair mean-field approximations as well as static Monte Carlo simulations. We determine the phase diagram of the model in the plane y_{A} versus temperature, where y_{A} is the probability that a monomer of the type A arrives at the surface. This phase diagram shows regions of active and absorbing states separated by a line of continuous phase transitions. Despite the absorbing state of the model to be strongly dependent on temperature, we show that the static critical exponents of the model belong to the same universality class of the directed percolation.

Moment ratios and dynamic critical behavior of a reactive system with several absorbing configurations

“…We also calculate the moment ratios between some moments of the order parameter to tune the critical point for each value of temperature. The critical point agrees with the values we have found in our previous work [1] and, for all considered temperatures, the dynamical critical exponents of the model are in the DP universality class. Special attention is also paid to the spreading dynamics, since the initial condition could affect the dynamical critical exponents δ, η, and ζ , as pointed out by Mendes et al [19].…”

“…From our previous results [1] concerning the critical values of the control parameter y A we calculate the ratios between some moments of the order parameter n v , which is the fraction of empty sites in the lattice. This approach was applied in the context of equilibrium systems [20] and, later, successfully extended to models out of equilibrium that present transitions to absorbing states [21][22][23].…”

“…The results showed that the critical exponents of the model are in the DP universality class, and that the absorbing state is unique, with the lattice completely poisoned by monomers of type B. The consideration of thermal effects into this model produces a multitude of absorbing configurations; however, the DP universality class is preserved regarding its static critical properties [1].…”

“…In a recent paper [1] we investigated the static properties of a reaction model between pairs of monomers A and B on a linear lattice, where we considered lateral interactions between nearest-neighbor adsorbed species as well as thermal effects. The phase diagram of the model was determined and we observed that, depending on temperature, the absorbing state is a poisoned state with different concentrations of monomers A and B.…”

Dynamical critical behavior of the Ziff–Gulari–Barshad model with quenched impurities

“…The critical exponents of the DP universality class were determined experimentally for the first time in a series of measurements performed on a turbulent liquid crystal system [9,10]. Transitions to absorbing states can also be found, for instance, in situations as traffic flow [11,12], transition to turbulence [13], spreading of a disease [14], as well as in catalytic reaction systems [15][16][17], which is the focus of the present work. Catalysis is a highly important mechanism employed in many industrial processes [18] and its modeling and simulation, by means of simple models, has became an important topic in the study of absorbing phase transitions.…”