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We investigate zero-temperature dynamics on the hexagonal lattice ” for the homogeneous ferromagnetic Ising model with zero external magnetic field and a disordered ferromagnetic Ising model with a positive external magnetic fieldh.We consider both continuous time (asynchronous) processes and, in the homogeneous case, also discrete time synchronous dynamics (i.e., a deterministic cellular automaton), alternating between two sublattices of ”. The state space consists of assignments of -1 or +1 to each site of ℍ, and the processes are zero-temperature limits of stochastic Ising ferromagnets with Glauber dynamics and a random (i.i.d. Bernoulli) spin configuration at time O. We study the speed of convergence of the configurationó tat time t to its limitó ∞and related issues.

Approach to Fixation for Zero-Temperature Stochastic Ising Models on the Hexagonal Lattice