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Published on: October 24, 2017
Exact phase diagram for an asymmetric avalanche process
V B Priezzhev1, E V Ivashkevich, A M Povolotsky
1Bogoliubov Laboratory of Theoretical Physics, J. I. N. R., Dubna 141980, Russia.
Abstract:
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.
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