The spectrum and the phase transition of models solvable through the full interval method

The most general exclusion single species reaction-diffusion models with nearest-neighbor interactions one a one dimensional lattice are investigated, for which the evolution of full intervals are closed. Using a generating function method, the probability that n consecutive sites be full is investigated. The stationary values of these probabilities, as well as the spectrum of the time translation generator (Hamiltonian) of these are obtained. It is shown that depending on the reaction rates the model could exhibit a dynamical phase transition.