Low-temperature coarsening of Ising ferromagnets

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.

A typical metastable state of the homogeneous ferromagnetic Ising model with Glauber dynamics on the 3-coordinated Cayley tree. At zero temperature these metastable states are actually stable. Shown are the first 4 levels of the tree. Spins in squares have their state uniquely determined by the states of the two "daughter" spins (black for + spins, red for - spins). Spins in circles are determined by the spin state of their parent (blue for + spins, magenta for - spins).


For details, see "Fate of Zero-Temperature Ising Ferromagnets", V. Spirin, P. L. Krapivsky and S. Redner, Phys. Rev. E 63, 036118-1--036118-4, (2001), and "Freezing in Ising Ferromagnets", V. Spirin, P. L. Krapivsky, and S. Redner, cond-mat/0105037 (submitted to Phys. Rev. E).