One-dimensional kinetic Ising model with nonuniform coupling constants
  A nonuniform extension of the Glauber model on a one-dimensional lattice with boundaries is investigated. Based on detailed balance, reaction rates are proposed for the system. The static behavior of the system is investigated. It is shown that there are cases where the system exhibits a static phase transition, which is a change of behavior of the static profile of the expectation values of the spins near end points. 
Mohammad Khorrami, Amir Aghamohammadi