Nonlocal Asymmetric exclusion process on a ring and conformal invariance

Abstract

We present a one-dimensional nonlocal hopping model with exclusion on a ring. The model is related to the Raise and Peel growth model. A nonnegative parameter $u$ controls the ratio of the local backwards and nonlocal forwards hopping rates. The phase diagram and consequently the values of the current, depend on $u$ and the density of particles. In the special case of half-filling and $u=1$ the system is conformal invariant and an exact value of the current for any size $L$ of the system is conjectured and checked for large lattice sizes in Monte Carlo simulations. For $u>1$ the current has a non-analytic dependence on the density when the latter approaches the half-filling value.

26 pages 26 figures

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• From interacting particle systems to random matrices
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Cited by in corpus (9)

• Infinite-dimensional meta-conformal Lie algebras in one and two spatial dimensions
• Correlation functions in conformal invariant stochastic processes
• Non-contractible loops in the dense O(n) loop model on the cylinder
• Laws of large numbers in the Raise and Peel model
• Large deviations of avalanches in the raise and peel model
• Critical phases in the raise and peel model
• Quasi-stationary states in nonlocal stochastic growth models with infinitely many absorbing states
• Stochastic processes with Z_N symmetry and complex Virasoro representations. The partition functions
• Cyclic representations of the periodic Temperley Lieb algebra, complex Virasoro representations and stochastic processes