Critical behaviour of a cellular automaton highway traffic model

We derive the critical behaviour of a cellular automaton traffic Row 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 nu(max) = 2, we determine the values of the critical exponents beta, gamma and delta 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 \rho - rho(c)\ and p in the vicinity of the phase transition point.