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 t
he problem based on the Master equation description is subsequently develop
ed, leading to full agreement with the microscopic simulations. [S1063-651X
(99)12710-7].