Dynamics of the symmetrically constrained Ising chain

The dynamics of the symmetrically constrained Ising spin chain, or symmetric one-spin facilitated kinetic Ising model, is investigated both by Monte Carlo simulation and by analytical mode-expansion methods. We confirm Fredricksonʹs argument that at low concentration of the facilitating up spins, the dynamics is governed by the diffusion of isolated up spins, but only for very low up-spin concentrations c ≤ 10−3. An adequate analytical treatment is obtained by a three-spin approximation, which describes the diffusion of pairs of isolated up spins.