AN EXACTLY SOLVABLE MAJORITY MODEL

A bichromatic majority model is presented and studied analytically. The mean value of one color, say black, dominant cluster size is calculated as a function of the occupancy probability p for the black plaquettes, while 1 - p = q is the occupancy probability for the white plaquettes. The model allows us to adopt different criteria for the definition of majority when a tie occurs, i.e. the numbers of black and white plaquettes are the same. This mean value shows a divergence with a critical exponent nu = 1. The model is equivalent to a random walk with an absorbing barrier and a non-perfect trap. A Monte Carlo simulation of the process is performed giving agreement with the theoretical calculations. Some comments on the results obtained with the renormalization group are presented.