In this paper, we study the evolution of the zero-temperature random field Ising model as the mean of the external field M increases from \(-\infty \) to \(\infty \) . We focus on two types of evolutions: the ground state evolution and the Glauber evolution. For the ground state evolution, we investigate the occurrence of global avalanche, a moment where a large fraction of spins flip simultaneously from minus to plus. In two dimensions, no global avalanche occurs, while in three or higher dimensions, there is a phase transition: a global avalanche happens when the noise intensity is small, but not when it is large. Additionally, we study the zero-temperature Glauber evolution, where spins are updated locally to minimize the Hamiltonian. Our results show that for small noise intensity, in dimensions \(d =2\) or 3, most spins flip around a critical time \(c_d = \frac{2 \sqrt{d}}{1 + \sqrt{d}}\) (but we cannot decide whether such flipping occurs simultaneously or not). We also connect this process to polluted bootstrap percolation and solve an open problem on it.
