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arXiv · 1305.4522

Nonlocal Asymmetric exclusion process on a ring and conformal invariance

Francisco C. Alcaraz·Vladimir Rittenberg
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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.

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Francisco C. Alcaraz, Vladimir Rittenberg. 2013-08-07. Nonlocal Asymmetric exclusion process on a ring and conformal invariance. https://doi.org/10.1088/1742-5468%2F2013%2F09%2Fp09010

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