Bidirectional Majority Vote

Each square is a spin (black = up, white = down). Each Monte Carlo step is two synchronous half-steps: first every spin takes the majority vote of itself and its vertical (up/down) neighbors, then every spin takes the majority vote of itself and its horizontal (left/right) neighbors.

Temperature adds noise: after each half-step, every spin's new value is flipped with a probability that grows with T, so the majority vote is exact at T→0 and washes out to a coin flip as T grows. Try quenching above and below to see the different phases!