Zero-temperature Glauber dynamics on Zd

We study zero-temperature Glauber dynamics on Z(d), which is a dynamic version of the Ising model of ferromagnetism. Spins are initially chosen according to a Bernoulli distribution with density p, and then the states are continuously (and randomly) updated according to the majority rule. This corresponds to the sudden quenching of a ferromagnetic system at high temperature with an external field, to one at zero temperature with no external field. Define p(c) (Z(d)) to be the infimum over p such that the system fixates at '+' with probability 1. It is a folkfore conjecture that p(c) (Z(d)) = 1/2 for every 2 <= d is an element of N. We prove that p(c) (Z(d)) -> 1/2 as d -> infinity.