A majority-rule model : real-space renormalization-group solution and finite size scaling

Through a simple majority-rule a statistical geometrical d-dimensional model (d can even be a fractal dimensionality) is formulated which presents a continuous phase transition as a function of a certain independent occupancy probability p. Both critical point pc and « correlation length » exponent ν are exactly calculated through real-space renormalization-group (with linear scaling factor b). The well-known finite size scaling hypothesis ν(b) - ν ∝ 1/ln b (in the limit b → oo) is analytically exhibited. A more rapidly convergent finite size extrapolation procedure is presented.