Journal of Statistical Physics, Vot. 66. Nos. 5/6, 1992, p. 1245-1276.
We present results on the Swendsen-Wang dynamics for the Ising ferromagnet
in the low-temperature case without external field in the thermodynamic limit.
We discuss in particular the rate of convergence to the equilibrium Gibbs state
in finite and infinite volume, the absence of ergodicity in the infinite volume, and
the long-time behavior of the probability distribution of the dynamics for
various starting configurations. Our results are purely dynamical in nature in
the sense that we never use the reversibility of the process with respect to the
Gibbs state, and they apply to a stochastic particle system with non-Gibbsian
invariant measure.