Lattice Models Solvable Through the Full Interval Method on Links

A two state model on a one dimensional lattice is considered, where the evolution of the state of each site is determined by the states of that site and its neighboring sites. Corresponding to this original lattice, a derived lattice is introduced the sites of which are the links of the original lattice. It is shown that there is only one reaction on the original lattice, which results in the derived lattice being solvable through the full interval method. And that reaction corresponds to the one dimensional stochastic non-consensus opinion model. A one dimensional non-consensus opinion model with deterministic evolution has already been introduced. Here this is extended to be a model which has a stochastic evolution. Discrete time evolution of such a model is investigated, including the two limiting cases of small probabilities for evolution (resulting to an effectively continuous-time evolution), and deterministic evolution. The formal solution to the evolution equation is obtained and the large time behavior of the system is investigated. Some special cases are studied in more detail.