Dynamical Critical Behaviors of the Ising Spin Chain: Swendsen-Wang and   Wolff Algorithms
  We study the zero-temperature Ising chain evolving according to the Swendsen-Wang dynamics. We determine analytically the domain length distribution and various ``historical'' characteristics, e.g., the density of unreacted domains is shown to scale with the average domain length as <l>^{-d} with d=3/2 (for the q-state Potts model, d=1+1/q). We also compute the domain length distribution for the Ising chain endowed with the zero-temperature Wolff dynamics. 
P.L.Krapivsky