Dynamical critical behaviours of the Ising spin chain: Swendsen-Wang and Wolff algorithms

We study the zero-temperature Ising chain evolving according to the SwendsenWang 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 <1>(-delta) with delta = = 3/2 (for the q-state Potts model, delta = 1 + q(-1)). We also compute the domain length distribution for the Ising chain endowed with the zero-temperature Wolff dynamics.