Critical behaviour of a cellular automaton highway traffic model

We derive the critical behaviour of a cellular automaton traffic flow model using an order parameter breaking the symmetry of the jam-free phase. Random braking appears to be the symmetry-breaking field conjugate to the order parameter. For vmax = 2, we determine the values of the critical exponents β, γ and δ using an order-3 cluster approximation and computer simulations. These critical exponents satisfy a scaling relation, which can be derived assuming that the order parameter is a generalized homogeneous function of |ρ-ρc| and p in the vicinity of the phase transition point.