Exact solution of the facilitated totally asymmetric simple exclusion process

We obtain the exact solution of the facilitated totally asymmetric simple exclusion process (F-TASEP) in 1D. The model is closely related to the conserved lattice gas (CLG) model and to some cellular automaton traffic models. In the F-TASEP a particle at site j in Z jumps, at integer times, to site j + 1, provided site j - 1 is occupied and site j +1 is empty. When started with a Bernoulli product measure at density rho, the system approaches a stationary state. This non-equilibrium steady state (NESS) has phase transitions at rho = 1/2 and rho = 2/3. The different density regimes 0 < rho < 1/2, 1/2 < rho < 2/3, and 2/3 < rho < 1 exhibit many surprising properties; for example, the pair correlation g(j) = satisfies, for all n is an element of Z, Sigma(k(n+1))(j=kn+1) g(j) = k rho(2), with k = 2 when 0 <= rho <= 1/2, k= 6 when 1/2 <= rho <= 2/3, and k= 3 when 2/3 <= rho <= 1. The quantity lim(L ->infinity) V-L/L, where V-L is the variance in the number of particles in an interval of length L, jumps discontinuously from rho(1 - rho) to 0 when rho -> 1/2 and when rho -> 2/3.