Mean-field study of the Swendsen-Wang dynamics

Nonuniversal dynamics introduced by Swendsen and Wang [Phys. Rev. Lett. 58, 86 (1987)] is studied in a mean-field Ising model. Numerical simulation data indicate that z, the dynamical critical exponent, is 0.98±{}0.08. A modified version of this dynamics in which only large clusters are flipped apparently gives the same exponent, although the amplitude is reduced by a factor of 1/2. In addition, a theoretical argument is presented which gives z=1 and provides insight into the dynamics.