Relaxation Times for Metastable States in the Mean-Field Model of a Ferromagnet

Relaxation from metastable to stable states is considered for a mean-field model Ising ferromagnet in which each spin interacts equally with every other spin in the system. Spins are chosen at random and flipped over with probability given by a suitable Boltzmann factor. Approximate solutions to the stochastic equations, confirmed by computer calculations on small systems, indicate a relaxation time increasing exponentially with the size of the system (contrary to one's expectation for a system with short-range interactions).