1305.4522 (Francisco C Alcaraz et al.)

Nonlocal Asymmetric exclusion process on a ring and conformal invariance    [PDF]

Francisco C Alcaraz, Vladimir Rittenberg

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 $u > 1$ a novel phase transition is observed when the density of particles approaches its half-filling value.

View original: http://arxiv.org/abs/1305.4522