A correlated majority model

We extend and solve analytically a bichromatic majority model including color correlation between nearest neighbor plaquettes. The behaviour of the one color, say black, dominant cluster size is studied as a function of the black concentration and the correlation degree. This mean value shows a divergence with a critical exponent v. We also define an order parameter m for the model whose critical exponent is β. We find v = β = 1 independent of the correlation degree. We present a Monte Carlo simulation of the process which gives a good agreement with the theoretical results