Reaction-controlled cooperative desorption in a one-dimensional lattice: a dynamical approach

The spinlike dynamics of immobile reactants in a one-dimensional lattice is analyzed for two representative systems involving cooperative desorption. An exact combinatorial approach is worked out. Its failure to reproduce the results of microscopic simulations is shown to be associated with the lack of sufficiently strong ergodic properties, as a result of which the final state depends strongly on the initial conditions. A dynamical approach to the problem based on the Master equation description is subsequently developed, leading to full agreement with the microscopic simulations.