Zero-Temperature Dynamics of Ising Spin Systems Following a Deep Quench: Results and Open Problems

We consider zero-temperature, stochastic Ising models σ with nearest-neighbor interactions and an initial spin configuration σ0 chosen from a symmetric Bernoulli distribution (corresponding physically to a deep quench). Whether σ∞ exists, i.e., whether each spin flips only finitely many times as t → ∞ (for almost every σ0 and realization of the dynamics), or if not, whether every spin — or only a fraction strictly less than one — flips infinitely often, depends on the nature of the couplings, the dimension, and the lattice type. We review results, examine open questions, and discuss related topics.