Exact phase diagram for an asymmetric avalanche process - art. no. 084301

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