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 $\tau$, where ln $\tau \propto N^{\frac{1}{4}}$ and so diverges as $N$, the number of spins, tends to infinity. The "ergodic time" ${\tau }_{\mathrm{eg}}$ satisfies ln ${\tau }_{\mathrm{eg}}\propto N^{\frac{1}{2}}$. 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.