Above you see an animation of the two-dimensional Ising model right at its critical temperature Tc, without external magnetic field. Black squares correspond to up-spins, white squares to down-spins (or vice versa, it does not matter). The lattice starts with all spins up, and then thermal fluctuations start to flip some spins down (and later up again). After some time you begin to see domains: spins tend to form groups of parallel spin (for energetic reasons). Due to fluctuations, these domains are not stable.
The initial condition of all spins up corresonds to a maximal magnetization. Right at the critical temperature Tc, this magnetization decays over time like a power-law: M ∝ t-β/νz.