Lack of Ergodicity in the Infinite-Range Ising Spin-Glass

The size dependence of slow relaxation processes in the infinite-range Ising spin-glass is investigated by computer simulation. Below the transition temperature, relaxation of variables which do not change sign under inversion of the spins is complete by a time τ, where ln τ∝N1/4 and so diverges as N, the number of spins, tends to infinity. The "ergodic time" τeg satisfies ln τeg∝N1/2. These results are consistent with a physical picture where barriers between free-energy minima in phase space have a height proportional to the square root of the number of spins to be flipped.