Here is a schematic picture of an L x L square lattice spin system which is stuck for a long time in a diagonal stripe configuration. Periodic boundary conditions are employed in both the vertical and horizontal directions. The diagonal state consists of a stripe of up spins (blue) and down spins (yellow) each of which wind once around the torus (square lattice with periodic boundary conditions) both in the circumferential and the toroidal directions. The width of these two stripes are both of the order of L. This diagonal stripe configuration has an anomalously long lifetime which scales as L^a, with a between 3 and 3.5. Amusingly, if the system reached the diagonal stripe state, the final state is the ground state of the system.

Time dependence of the survival probability S(t) on L x L square lattices. Main graph: S(t) versus t/M₁₀ to highlight the long-time exponential tail. Here M_k=< t ^k>^1/k is the kth reduced moment of the time to reach the final state. Scaling sets in after S(t) has decayed to approximately 0.04. Inset: S(t) versus t/M_1/10 to highlight the scaling and the faster exponential decay in the intermediate-time regime. This graphs shows that there are two distinct time scales which govern the behavior of S(t).

A typical metastable of the three-dimensional Ising model on a finite cube with periodic boundary conditions in all directions. One phase of the spins are represented as blue unit-size cubic blocks. This spin cluster has a sponge-like topology so that there are no convex corners. The red blocks denote "blinker" spins which can flip indefinitely with no energy cost.