Exact phase diagram for an asymmetric avalanche process

The Bethe ansatz method and an iterative procedure based on detailed balance are used to obtain exact results for an asymmetric avalanche process on a ring. The average velocity of particle flow, v, is derived as a function of the toppling probabilities and the density of particles, rho. As rho increases, the system shows a transition from intermittent to continuous flow, and v diverges at a critical point rho(c) with exponent alpha. The exact phase diagram of the transition is obtained and alpha is found to depend on the toppling rules.