DYNAMICS OF THE INFINITE-RANGED POTTS-MODEL

We formulate a theory of single-spin-flip dynamics for the infinite-range q-state Potts model. We derive a Fokker-Planck equation, without diffusive term, from a phenomenological master equation. It describes the approach to equilibrium of the time-dependent probability density and thus generalizes Griffiths' (1966) result for the Ising model. We particularly compare the dynamic evolutions of q = 2 and q = 3 systems when sinusoidal external fields are applied. In the case q = 2 we find evidence of a nonequilibrium phase transition and for q = 3 period doubling bifurcations are observed, yielding a good estimate of Feigenbaum's universal exponent.